I cannot really see Britain taking that risk in 1915 or 1916. It's not like they had plenty of divisions sitting around with nothing better to do
. And the Royal Navy trying to get control of the Baltic is really going to make the day of the "Kleinkrieg" strategists in the German HighSees Fleet.
Especially though, if you add the political and diplomatic risk of Britain attacking two neutral countrys. The U.S. had a significant Scandinavian population and if not only Sweden joins the CP, but also Norway and Denmark get attacked by the Entente, they might snatch defeat from the jaws of victory in the Propaganda War.
I was thinking of the forces deployed in the OTL Dardanelles, which eventually involved some 480.000 men of which about 80.000 were French. That ought to be enough, it is hardly possible to deploy more men in Scandinavia. But it all preconditions that Copenhagen can be taken. It will at least require a pronounced will to take heavy casulaties. At least half the force + considerable naval forces would be needed vs. Copenhagen
I will not outrule the possibility of Norway joining the Entente, it afterall was only in 1905 they gained full independence from Sweden, and not in a cordial atmosphere. Some Swedish remarks about reconsidering the independence and...(well, if they can join the CPs, why not this too?).
It will anyway be very bloody, but I guess the main problem is taking Copenhagen fast enough to keep the Germans from landing strong forces in Sweden and throwing the Entente out of Norway, or to avoid total failure before that.
There were Entente plans of Baltic adventures, and Adm. Fisher at least claimed that the big light cruisers of the Courageous class were specialised for Baltic operations. At least one of the plans involved gaining control of the Baltic and thereafter landing a Russian Army on the coast north of Berlin.
If Sweden already has joined the CPs and the Entente has landed in Norway, I guess the Danish government by Berlin will be asked to stuff neutrality, and I doubt they will have any other option. Germany certainly wasn't popular in the broad Danish public, who had 1864 in fresh memory, but nobody really questioned the Government's policy of staying close to Germany, perhaps because Denmark anyway would be close to Germany. Next there were no recent tradition for alliance with UK, on the contrary. UK had been THE enemy in the Napoleonic Wars and of no help in 1864.
Regards
Steffen Redbeard