I mean it seems stunningly unlikely.
But here's an idea. In the aftermath of the defeat of the fourth coalition, The UK, Sweden and Portugal were just about the only three nations still opposed to napoleon.
In OTL Sweden got beaten up by russia and denmark and dropped out whereas portugal and spain managed to hold on thanks to british support.
Now lets say in ttl things go the other way around. Napoleon keeps the spanish army loyal and crushes portugal but sweden stays in the game despite losing finland to russia and denmark norway flips sides.
At this point, napoleon wins a few major victories and dies. His successor negotiates peace on the basis of the current borders.
The result is pretty much all of europe is dominated or allied to france apart from scandinavia and the uk. Who as the only representives of the old system form close economic and political ties together, the german danish border and swedish russian borders become highly militarised due to mutual distrust and british soldiers are sent out to man the borders relatively reguarly to show their allies the brits can be trusted. This leads to many brits marrying scandivanians and a certain cultural blending.
Then a king dies without a heir and someone suggest the kalmar option. Europe is looking particuarly threatening at the time, scotland, ireland and norway are already areas of the kingdom used to different laws but the same king and the idea of a union between the three begins to become popular, if all three kingdoms kept their laws and parliaments but had a single king and joint foreign policy it might even work. Denmark would love a new kalmar union, sweden would welcome a step back from the absolutionist vasa monarchs and the uk don't want to be cut out from the continent all together.