With a POD after 1812 if you choose to accept you must create a United Kingdom of Scandinavia which includes all of Denmark, Norway, and Sweden. Which is formed out of the aftermath of the Congress of Vienna.
The century-old, deep-seated passionate hatred between Sweden and Denmark would make any such proposition highly problematic. In the aftermath of the Finnish War, Sweden might decide to pick a Danish prince instead of Bernadotte as an heir, but I guess that most of Swedes whose opinion mattered would have preferred to see the country burn rather than beiong ruled by a Dane.
You know they picked a Danish prince before Bernadotte?
http://en.wikipedia.org/wiki/Charles_August,_Crown_Prince_of_Sweden
The way I heard it, it was for similar reasons Wilhelm I of Prussia rejected being Emperor of the Germans - he was fine with getting the title, but he wasn't fine with all the ideas of parliamentary power and making certain the king didn't coup himself absolutism again floating aroundAnd before Charles August, they asked the King of Denmark (http://en.wikipedia.org/wiki/Frederick_VI_of_Denmark) to be the heir, actually. But for whatever reason, Frederick refused to take the title.
You know they picked a Danish prince before Bernadotte?
http://en.wikipedia.org/wiki/Charles_August,_Crown_Prince_of_Sweden