Well, I mean, err-...
I have for the longest period of time been working on a timeline where both Sweden intervenes in the second Schleswig-Holstein War (well, a version of that conflict, the PoD is in 1770), and there is a United Scandinavia.
That being said, I honestly do not think that a United Scandinavia is anywhere near as easy to achieve as a United Italy or a United Germany. I certainly do not think that Swedish intervention alone can accomplish that, indeed, I am uncertain that Swedish intervention on its own can actually help Denmark win the war. The Prussians have the Austrians on their side, and basically all of Northern Germany. The way I see it, the only way the outcome of the war could have ended up differently (providing Prussia still has the support it had OTL) had been if Lord Palmerston had decided to act.
And he didn't.
He admitted that his sympathies were on the side of the Danes, but he felt that there was no clear British national interest at stake in the conflict (which is a point that cannot be refuted) and so he couldn't in good conscience commit British blood and treasure to the cause. He also said that he wasn't too keen on sending the Royal Navy into the Baltic Sea in winter, which strikes me as a fairly odd comment to make. Surely the Royal Navy ought to be able to handle that.