Ok let's see, the Tsar will still be assassinated ending the League of Armed Neutrality, therefor ending the threat to the British.
I still see Denmark as trying to stay neutral, it worked for them for the few decades or so before 1801, and I think they wanna keep it that way. the interesting part is what happens in England, is Nelson sacked, for ignoring an order to withdraw from superior? (the famous, putting his blind eye to the telescope) what happens at a potentially very different Trafalgar, and most importantly when the British defeat the Spanish/French fleet in the ATL Trafalgar, what will the British do about one of the only European navies left challenging them (which also happened to defeat their own navy a few years earlier)
Certainly the Danish navy was a quite capable force, and compared to the Napoleonic French fleet, the Danish navy had experienced seamen (mostly Norwegian, which were not present in the battle of 1801) But the sheer quantity and quality of the British navy will definitely be able to defeat the Danish one, if they decide to do so. The question is would they? I don't know enough of British politics etc. to give a educated guess upon the chance that they would try to negotiating with Denmark-Norway or if they just will send a larger force towards Copenhagen in an ATL 1807 (which might not end in the bombing of Copenhagen, but instead a second large naval battle between a fully outfitted Danish navy against the British) It would however probably mean the defeat of the Danish navy, making the Danish state allying with France, which will then probably mean the starvation of Norway, bankruptcy of the Danish state, and finally the exchange of Norway for the Duchy of Lauenburg (same outcome OTL)
A (in my Danish eyes) rather unfortunate and kinda boring outcome of a victory over Nelson in 1801.
A much more interesting outcome would be negotiating between Denmark-Norway and the British. If Denmark end up in the British camp, we would see no loss of the navy, no bankruptcy, and more importantly an intact Dano-Norwegian Kingdom, meaning a rather different Scandinavia than OTL, while probably not changing much of the rest of European history.
Thoughts?