The answer to a part of this question is actually quite simple, but if this answer breaks the rules, feel free to delete it. I don't know anything about what type of paganism existed in Schleswig at the time, but I can answer the part about paganism in the region.

Your basic assumption is unfortunately incorrect. Schleswig is on the other side of Dannevirke, a fortification near the root of the Jutland Peninsula, and while we don't know exactly when it's from (400 AD-800 AD probably), it traditionally marks the border of what would be considered the realm of the Danes. Danes are mentioned in sources already around 500 AD, and around 800 AD it was probably the most consolidated realm north of the Frankish Kingdom. Those facts should probably indicate that Christianizing the Schleswig area wasn't a simple task at the time, although we have very few Danish sources about those times, what with proper writing and record-keeping being introduced to the Danes with Christianity (Yes runes were a thing, but record-keeping, messages, letters etc mostly came with Christianity).
The Danes weren't Christianized before 965, when the monk Popo arrived at the royal court, according to the Jelling Stone, a rune-stone placed in the king's town Jelling by King Harald Bluetooth. Even then, it likely took the better part of a century to stamp out paganism in Danish areas completely.

In short, Schleswig was pagan around 965 because the rest of the Danes were pagan as well (even if calling all people north of Dannevirke Danes isn't necessarily 100 % accurate). Parts of the ruling class converted with the king, but converting the people was a longer process.

Sources:

Aarhus University Learning material for its course on Danish History: https://danmarkshistorien.dk/ooc/ny-indledning/tiden-foer-1050/

First I would like to expand on Schleswigs history. In 965 the city that we today know as Schleswig didn't really exist. Instead (at least here in Denmark) we characterize the city that existed in 965 as Hedeby/Haithabu, though as you see in the ibn Yaqub it was also known as Schleswig at the time. The modern city of Schleswig was only founded after Jutland had been ravaged by wars between Harald Hardrada and Svend Estridsen. It was situated on the north banks of the Schlei, while Hedeby was situated in the south (though they were situated very closely to one another, and Schleswig was probably founded by people driven from Hedeby)

According to Frankish sources the city had been established by a Danish king known as Godfred in 808 by resettling merchants from a Frankish city by force. How much truth there is to this acount is difficult to tell. We know there had been a city at Hedeby since the 700s and as far as I know we can't pinpoint a great expansion to 808. However this account does show that Hedeby was not considered under the control of the Frankish emperor. At least not wholly.

I should mention that the status of the relationship between Denmark and the Frankish Empire is murky. The situation in Denmark is not known. We have no idea how much territory Godfred held in 808, nor if he considered himself a vassal of the Frankish Emperor or a wholly sovereign ruler. We are also uncertain how the Franks viewed the relationship - but they definitely found Godfred to be acting with hostility - the forceful resettlement of merchant was seen as an attack similar to other attacks by the Norsemen (what we today would consider Viking attacks). Later on, by 965 we are still uncertain how this relationship should be understood since there are very few Danish sources before 1000.

So all in all we don't find that the Franks held any significant amount of power over Hedeby at the time of 808 which is after the Saxon Wars had concluded (though I am not very knowledgable of the Saxon Wars). That is to say, Charlmagne might have christianized northern Germany - but he probably didn't reach Hedeby, which was under control of some Danish petty king. However the Frankish and later the Holy Roman Empire would play an important factor in converting the people of Hedeby.

In the early 800s a mission was established in Bremen with the goal of converting Scandinavia (and other parts of northern Europe). The most important figure in the first half of the 800s were probably the monk Ansgar, who established the first church in Hedeby. He was only able to do this by bargaining with the pagan Danish king, further cementing the fact that the christian empire to the south didn't hold a lot of power this far north.

This resulted in Hedeby, being the closest city in Scandinavia to the empire, becoming probably the most christian city in Viking Age Scandinavia. It was home to the first church in Denmark and there have been found a large amount of ornamental crosses. Famously one find at Hedeby was a mold that could be used to both create ornamental crosses and hammers (hammers are usually considered a pagan symbol alluding to Thor's hammer Mjølner, but there have been recent discussions within academia as to whether or not this is really true).

It was also most likely pressure from the Holy Roman Empire that resulted in Harald Bluetooth converting to christianity around the same time ibn Yaqub visited Hedeby around the 960s. However the king converting and officially "christianizing" the danes didn't actually result in most people becoming christian. The process of christianization was slow and gradual. Even 100 years later the amount of churches around the country was rather limited and most of them were small, most likely built for the elites of society.

As for which god Sirius was - I don't know. I wasn't able to find out exactly the word ibn Yaqub used in the original language of the text. It is very likely that he was "translating" the name of the god into the name of a god his target audience would have known about rather than using a germanic/norse name. But this is just speculation.

​

TL:DR: Schleswig wasn't christian at the time because it had never been christianized by the frankish emperor. The city had mostly been controlled by Danish kings rather than the emperors of the Frankish and Holy Roman Empires, though the exact nature of the relationship between Denmark and these empires is murky. They did however play an important part in slowly converting Hedeby's population over the next couple of centuries.

Not quite what you were asking about but here is an (old) answer about post christianisation paganism if it helps.