There is a flaw in the premise of your question. There is no such thing as "pre-Catholic Christianity" in Scandinavia. The papal curia went through a period of centralization in the High Middle Ages which gave it much more direct control over bishops than it had had previously. Someone here might be able to speak to how that affected 12th century Scandinavian Christianity, but it is not a case of pre-Catholic and Catholic: Both periods are equally Catholic.

Sorry for the really late response.

Tl;dr: If you are absolutely confidant with the basic background of the hierarchical institution of the Catholic Church, please just skip directly to the Part II (the circumstances of local churches before the parish) or the latter part of Part I (Adam of Bremen, staunch defender of the missionary traditions of his superior, archbishop of Hamburg-Bremen).

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[Part I]

First of all, I'm afraid that the cited description of wikipedia can be a bit misleading, as already pointed out by /u/Kelpie-Cat.

the realms of Denmark, Norway & Sweden's archdioceses only became directly responsible to the pope around 1104, 1154 & 1164 respectively......

There had been no "archdiocese" of either Denmark, Norway, Sweden prior to the dates in question, namely:

• Before 1104 CE, Scandinavia had been a part of the church province (archdiocese) of Hamburg-Bremen in Germany, at least according to the claim of the archbishop of Hamburg-Bremen. It does not mean that Scandinavian bishops had not nominally been subjected to the papal authority, however. As I summarized before in: To what degree World the early church of Scandinavia be connected to the church of the continent and the papacy?, some "reformist" popes had already begun to try to negotiate with rulers (kings) in Scandinavia directly in course of the 11th century. The year 1104 was in fact terminus ante quem (mentioned as the archbishop in the official papal document) when the bishop of Lund in medieval Denmark (now Sweden) was officially ascended to the status of archbishop who was to have a jurisdiction over the new, fully independent church province (archdiocese) over the whole Scandinavia (as well as the North Atlantic) "directly" under the Papacy.
• In 1154 or a bit earlier (in 1152/3), bishoprics of Norway and those in the North Atlantic from the Isle of Man to Greenland was in turn separated from the church province of Lund to form an independent church province (archdiocese) under the new archbishop of Trondheim/ Nidaros (the latter name would first be used by the ecclesiastical document since around 1170, though).
• In 1164, then, bishop of (Gamla) Uppsala, Sweden was finally ascended to the archbishop who was to have a jurisdiction over the bishops "of the Swedes and the Götes", and to be separated from the archbishopric of Lund, though the archbishop of Lund would still retain some rights as "Primate" over this new archbishop (former his suffragan) of Uppsala (down to when and to what extent it was of real significance the opinions of researchers differ, though).

The acknowledgement of the official status of the independent archbishopric within the kingdom by the Papacy in Rome constituted, so to speak, an ultimate political as well as religious goal for newly converted rulers in high medieval Northern and Central Europe, as illustrated in Eiríksdrápa, St. 25, composed by Icelandic Poet Markús Skeggjason and dedicated to King Erik Ejegod of the Danes (d. 1103/ 04):

"The energetic lord [King Erik] had an archbishopric established in Denmark a short way from Lund, which all the people of the ruler’s land worship in the Danish tongue [Scandinavian languages general]. The prince advanced the holy kingdom; one can hear that the very capable Ǫzurr [Archbishop Asser of Lund, bishop of Lund from 1089-1103/4, as an archbishop, from 1104? to 1137] was ordained bishop; the trier of freeholders [= God] shows him the path to the heavens." (The translation is taken from the official site of Skaldic Poetry of the Scandinavian Middle Ages)

If you are really interested in this topic of the church history, the comparison between the rise of bishopric of Gniezno (Poland) onto the archbishopric and the long pre-history of that of Prague (Czech) might be interesting (it took centuries for the latter to be finally elevated to the status of the archbishop in the 14th century).

While the foundation of, or the rise of former bishopric (suffragan under another archbishop) onto the new, independent archbishopric has usually required the official approval by the Papacy (at least since the turn of the millennium), the foundation of the bishopric, or the invitation of the missionary bishop was more casual (as we'll see below), and the concept of the strict territorial division of "missionary bishopric" among missionaries of diverse origins would be firmly established first in Early Modern Period (the first half of the 17th century).

Before that, especially in Early Middle Ages, missionaries (including missionary bishops) of diverse origins (under different superior church authority, archbishop) could engage with preaching and taking care of pastoral care for newly converted people in the almost same area at the same time. On contrary to the claim of Adam of Bremen (see below), the inflow of Christianity as well as missionaries in Viking Age Scandinavia also almost certainly had plural routes from different origins.
German and English (Anglo-Saxon) were two major routes, but even as for the first, the German route, the church of Hamburg-Bremen could probably not monopolize the mission to the Scandinavians at least since the 10th century, recent studies suggest.

To give an example, "Missionary Poppo", who allegedly played a crucial role in the baptism of King Harald Bluetooth of the Danes (d. 987), in some traditions like this famous gold alter plate of Tamdrup (about 1200), is possibly identified by Michael H. Gelting as Folkmar, later archbishop of Cologne (Gelting 2010). If we accept this hypothetical identification, Archbishop Bruno of Cologne (brother of Otto the Great) as well as clergy from the church of Cologne was also likely to have involved with the promotion of Christianity in Denmark.

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Adam of Bremen, staunch defender of the missionary traditions of his superior, archbishop of Hamburg-Bremen

Adam of Bremen, a canon of the cathedral chapter of Bremen, wrote manners and customs of Northern peoples as well as the history of missionary activities conducted by "his" archbishops and clergy since the 9th century in his work, titled as History of the Archbishops of Hamburg-Bremen, in around 1075. This is our first and foremost written source for missionary activities and early Christianity in Scandinavia in the 11th century, and Adam is a historian as well as a kind of the first ethnographer for the northern peoples in this work. This source can also sometimes be very tendentious in its almost very critical topic, Christianization of the Scandinavians itself, however.

Many written work in the Middle Ages have the possible particular reason of being written (causa scribendi - Cf. Althoff 2003 (1988)), and Adam's work was no exception: Althoff surmises that the primary purpose of the work is to provide new Archbishop Liemar (r. 1072-1101) with the justified role model of his predecessors who also established the predominance of missionary fields.

Other scholars like Henrik Janson and Volker Scior (Janson 1998; Scior 2002), suggest one more important motive to compose this work - the privileged status of (Hamburg-) Bremen, once allegedly called as "the equal of Rome and sought by people in troops from all parts of the world, especially by the northern peoples...... (Adam III-lxxiii, the translation is taken from (Tschan trans. 2002: 180) are just being threatened by both sides, the Papacy in Rome and some rulers in Scandinavia, such as King Svend Estridsen of the Danes (d. 1076) who wished to have more direct relationship with Rome, bypassing Hamburg-Bremen. On the eve of the Investiture Contest, the Reformed Papacy, represented by Cardinal Hildebrand - later Pope Gregory VII - became increasingly wary of too powerful local archbishop who was also very friendly with local ruler, and new Archbishop Liemar of Hamburg-Bremen was just one of such proteges of so-called "Imperial Church System" under the auspice of King Henry IV of Germany.

In order to justify this mission of "his" archdiocese, according to these recent research, Adam sometimes judges "Good/ Bad" Christian primarily in accordance with the loyalty/ acceptance of the jurisdiction of Hamburg-Bremen. A few local rulers who especially sought to be independent from Hamburg-Bremen (though necessarily want to apostate himself) and accepted missionaries from other churches than Hamburg-Bremen were often labeled as bad Christian (either unmotivated like King Emund or superstitious like Olav Tryggvason - see Everybody loves Olaf Tryggvason. Why?), or, in the worst case, categorized as an pagan/ apostate (King Svend Forkbeard of the Danes).

Other possible sources, both Scandinavian and non-Scandinavian (German and English) are not without flaws to use them to reconstruct the 11th century Scandinavian society - to give an example, what extent can we trust the prescriptions in the law book only extant in the 13th century manuscripts for the initial state of Christianization in the 11th century?

Anyway, this is the most basic point to be wary of to read the work of Adam of Bremen, basic source of 11th century Scandinavia politics as well as Christianization.

[To be continued to Part II]

(Edited): proofreads and corrects some grammatical mistakes and typos to clarify the meaning better.