One of the main problems was that the Danes never saw the peasants as a power factor, because they were not in Denmark, but they were in Sweden.
The standard tactic of the Danes was to disenfranchise the nobles by putting their own loyal men in the castles and bishop palaces. If Sweden had been like Denmark, this would probably have been pretty smart. However, this angered not only the Swedish nobility, but also the peasants.
The peasant militia in Sweden at these times was quite a good force - not as good as Landsknecht mercenaries, especially not in open combat, but they used high-quality swordspears specifically designed to fight both mounted knights and pike- and halberd-wielding infantry. This was combined with a bow or later an crossbow and a sword or an axe as well as armour - ususally less than modern (scale or chainmail, helmet and bracers).
With superior numbers and good leadership, the Swedish peasant militia could take on the best forces the Danes could produce in open combat, like at the Battle of Brunkeberg 1471, where the forces under Sten Sture the elder completed an advanced manouvre and cut of a large part of the loyalist army (that was mostly Swedes too, but included a large amount of Danes and German mercenaries and the Danish King Kristian I). The Swedes were also early adopted of gunpowder, using arquebuses and cannons from the mid-1450s.
The Danes and Germans, especially the Germans, were not used to this and never really learned it either. For this scenario to be valid, you need to deal with the dual problem of Swedish nobility wanting more power for themselves and having their own interests and struggles (industry, Novogorod, Finland etc) and the Swedish peasantry's militancy, dedication to their old rights and strong armament and organisation.