67th Tigers
Banned
First, Sweden actually has to do something, a formal declaration of war backed by no concrete military action isn't going to earn much.
67th Tigers, just what would Denmark be getting out of all this? Risking much of her military and fleet to strengthen Sweden doesn't strike me as being of use to Copenhagen.
There's also the long term as this pretty much ensures that the Russians will rearm as rapidly and massively as possible, just as the French or British would if they suddenly had an enemy border in artillery range of their capital city's outskirts, not to mention making future relations between the Anglo-French and the Russians much more problematical.
They gained security for Schleswig-Holstein. They were to extract a British alliance guaranteeing it again the German Federation (or that was their intent). It was also about being on the "winning side"; Austria had delivered an ultimatum, Spain had come over to the British, and by winter 1855-6 the whole of Europe was lining up to kick the Russians.
As Lambert (The Crimean War: British Grand Strategy against Russia 1853-6) points out in his discussion of the Baltic plans for 1856, Sweden always intended to declare, but were holding out for a little while to get a better deal, but held out so long the war ended and they got nothing.
The entire British policy for the post-war settlement was to make Russia too vulnerable to contemplate another adventure; by insisting on the disarmament of Forts etc. the British were guaranteeing their ability to strike cheaply at Russia. A force within striking range of the capital would affect this even better (Neilsen, lecture to Joint Command and Staff College, 2007).