It would probably be a risky business even if they managed to grab a colony somewhere.
Historically most of the fighting in around the baltic where backed by other nations, wanting to keep the struggle for the baltic trade going. Nations who were, for the most part colonizing nations.
If Denmark manages to upset someone it could mean support for Swedish revanchism during the 18th century.
Actually Denmark had its colonies seized by Britain a couple of times even during the Napoleonic wars but got them back following termination of hostilities!
That wasn't the issue.
As already said getting the hinterland of Danish Gold Coast turned into a thriving agricultural area could have changed the perception of colony in Danish ruling circles and made for further investments. Problem was that the slave traders were still powerful when this was attempted and allegedly killed off the first prospector effectively killing off the colony.
The West Indies was a back yard with planters trying to rip off a profit caring zilch of Denmark - most was non-Danes. Only late in the history did government take a real interest there but then it was too late.
Making it viable would need a very early change in who's setting up plantations or a plan when the slaves are emancipated as to whats up now!
One positive was that Charlotte Amalie was actually the second city of the Kingdom and a major trade hub in the Caribbean!
The Indian colonies were merely trading stations - factories or forts - too scattered and too small to make a difference. Their raison being of course to trade the valuable spices etc. from India but also secure the route to the real bonanza market - China!!!
At all times the resources allocated were too few to matter being the energies of individuals intereste in making a profit and the state not really being interested in settling the areas but reaping a profit too!
No wonder as the King wanted to live in splendour and needed to finance his wars with mostly Sweden so income was needed; not costly overseas establishments.
What would be needed was more government/state/King interest in long term development of colonies beyond mere profit reaping; a surplus of manpower to populated said areas and not spending limited resources on immensely costly wars.