What guilds would have the most political clout in a medieval city? Skandanavia, in particular.
Simply those with the most economic clout. For example in late medieval Flanders and Brabant the guilds associated to the cloth trade (the most important industrial sector in these regions, often putting 50 to 70% of a city's people to work), would have the most political clout. It was often under the influence of the weavers that the guilds there revolted against local rule.
Of course there are other ways to get political clout, such as alliances with local government, but those were also mostly dependent on the economic power of the guild.
I don't know which guilds in Scandinavia were most important economically.