I'm not entirely sure what POD could lead to Denmark joining one of the Coalitions, perhaps A.P. Bernstoff lives on for another decade and makes some wiser diplomatic choices.
I don't think this would have a huge impact on the larger war.
I guess Napoleon would surely occupy Jutland, but I believe the intact Danish navy would keep the rest of the Kingdom out of reach.
With the evidently more favorable position at the end of the war, could Denmark make some gains instead of the OTL loss of Norway along with bankruptcy.