Ah, I see. Well either way, Denmark (via Norway) had had control of Greenland for a long time by that point, and Greenland was still near-useless as either a trading post or military base, so it was near-ignorable for the British.
Control? The 1721 missionary expedition was to make sure the Norse on Greenland had not fallen back into paganism, but instead they found that none of them were left. We of course had a claim to Greenland through Norway, but we didn't have any control until then. Not unless I've been misled at least!
It's true that the Scandinavians often did seem to find failure in even the most promising of positions, you're right - although this kind of hindsight was something that no-one, Danish or British, had at this point, regrettably.
Considering the way things went in OTL, any change seems likely to fall on the side of improving the Danish position.

Not assured obviously, but with a hit-miss-ratio like Denmark had, it shouldn't hurt to get some inspiration from Britain instead of Germany.
It's still that Denmark be on the front foot in its foreign policy, though. And heck, if the Danes want to screw stuff up and fail to meet their potential, it could even make life a little bit easier for the British. A Denmark that starts to actually dominate the Baltic is a Denmark that will start being unsatisfied with just concentrating on the Baltic, and will want to expand its influence into British areas...
Yeah, the best option for the British would probably be for the Danes to become a counter to the Russians in the north, but never strong enough to actually dominate anything. That way they're more likely to keep their focus in the Baltic instead of deciding that Indo-China would be a nice jewel in the crown.
I do agree with Sian that Denmark would probably focus more on the North German(not Germanic!

) states if its position was strong enough.
That sounds perfectly logical to me. I couldn't speculate on how much it would change their fortunes, though.
Well, a richer Denmark-Norway might retain more of its population? In OTL, both Norwegians and Swedes fled in pretty large numbers to the US, which they might do in smaller numbers here. Certainly the Norwegians, but some of the Swedes passing through Denmark might decide not to risk the Trans-Atlantic journey if conditions in Denmark were good enough.
On the other hand, factory work is pretty terrible compared to getting your own farm in Minnesota.
Getting a touch of modernity injected might also protect against some of the weird anti-modern ideas that infected Denmark in the mid 19th century. Generals deciding that rifles that fire quicker are a dumb idea, because the soldiers will just waste ammunition, is not exactly the road to success.