I interpreted OP's question as the possible Danish-Scandinavian reaction against the resurrection of Wessex royal line in England, represented by King Edward the Confessor.

Tl; dr: Scandinavian (mainly Danish) political circumstances in 1030s and 1040s were even more chaotic than English ones after the deaths of King Cnut the Great of the Danes and his sons, so they rather sought help or allied with the new English ruler to forestall another throne contender of the Danes.

I summarized some basic elements of the political turbulence in Scandinavia since the last decade of the reign of Cnut and his death below:

• What held the North Sea Empire together, and why didn't it last past the life of Cnut?
• Anglo-Saxon Historians - Would the Godwin / Godwinson dynasty be able to call upon political support / military support coming from Denmark?

I also re-arrange the main problematic points from these threads below:

• The extinction of the direct male line of the Norwegian Earl of Lade family by the sudden death of Earl (jarl) Håkon of Lade-Northumbria in ca. 1030 was indeed almost critical blow to Cnut's Scandinavian policy: Cnut lost the most promising regent in Scandinavia as well as the heir of the traditional Norwegian supporter of the Jelling dynasty of the Danes in Norway. This also triggered the power struggle among the Norwegian magnates, and it un-stabilized Danish rule further in Norway.
• The prevalence of young, inexperienced but legitimate throne claimants of Norway and the Denmark: Magnus the Good (d. 1047), and three sons of Cnut, namely Hardeknud (Harthacnut) (d. 1042), Harold Harefoot (d. 1040), and further, Regent Sven of Norway (d. 1035) were all in teens when Cnut was died in 1035. It means that they had to rely much more on the goodwill of the Scandinavian magnates than Cnut, and their political inexperience allowed more free hands to the power struggle among the magnates themselves. To give an example, some later Scandinavian sources tell us that the Norwegian and Danish magnates mediated the two young claimants of the throne, namely Hardeknud and Magnus the Good, in ca. 1037/ 38 to conclude the agreement that who would outlive another would take the deceased's kingdom and throne.
• Later King Svend Estridsen of the Danes (r. 1047-76) and King Harald Hardrada (r. 1045/ 47-66) of Norway was slightly older than them, but both of them had the legitimacy problem in common, namely the legitimacy claim to the rulership only by the female line. They had another (but different) weakness in legitimacy respectively. Svend's father, Ulf, was a traitor to the late King Cnut, and Harald had been away from his homeland and in Russia and in Constantinople in late 1030s.

Thus, these Scandinavian (Danish) throne contenders were mostly full of themselves, in a sense, and it is related in Anglo-Saxon texts that both sides of throne claimants of the Danes after Hardeknud, Magnus the Good and Svend Estridsen, sent envoys to the new King Edward of England to secure the peace, and as for the latter (Svend still had two living brothers in England then), further asked the help in form of fleets from England, though this request was declined.

I cited some relevant references in the linked thread, these difficult political circumstances in Scandinavia might be a bit difficult to follow only based on Anglophone (written in English) literature.