Hmmm...with certain cultural changes, it's probably possible for Pan-Scandinavianism to become a real thing...with an 1814 POD, I would try to get Sweden to somehow hang onto Finland, and thus Norway stays with the Danish crown. From there, Sweden and Denmark begin to cooperate much more politically and economically, and ultimately unify during the Era of Nationalism...though how that can be done while getting over Swedish concern of a New Kalmar Union is anyone's bet.
Meanwhile, the Italian unification wars become a lot messier, and Prussia gets drawn in while unprepared. They are roundly defeated by the French, and the Danes/Scandinavians take advantage of the chaos to integrate Schleswig-Holstein. ITTL, Prussia never quite re-emerges as a great power, and Austria is too crippled dealing with the obstinate Magyars to take advantage of the power vacuum in Germany. From there, Denmark benefits from an influx of immigrants from Germany, many of whom went to America OTL, helping to alleviate the demographic disadvantage. From here, during the era of colonization/scramble for Africa, Scandinavia picks up a fair share of African and other territories, likely what Germany got OTL. At this point, they are probably a power comparable to Italy and stronger than Prussia, so second-tier but still arguably technically a great power. I wouldn't be surprised if they have one of the best navies in Europe after Britain, though.
However, I don't know if there's any POD that would make this happen or how plausible it is.