IOTL, the Danish Virgin Islands were sold to the US in 1916 which culminated several attempts dating back to the 1860s to transfer the islands to American hands; the impetus for the conclusion of the sale was a fear that somehow the High Seas Fleet might seize the islands (never mind that Denmark was a neutral at the time) for use as a U-boat base in the western Atlantic. Suppose, however, the more anti-war members of Congress, particularly the Senate, which had to approve the treaty, blocked the sale and transfer?
Now fast forward to 1940: the islands are still Danish, and presuming the sale had no butterflies in Western European events, the Wehrmacht overruns Denmark. Do the islands:
• Become a home-in-exile for the Danish royal family?
• Get seized by the US on whatever pretext might be cobbled together to prevent Germany from grabbing them?
• Get seized by Germany and converted to a base in the Caribbean and western Atlantic for U-boat warfare?
• Have some other chain of events transpire?
I might add that this third option could well be a worst case for the locals, since today the island's population is roughly 3/4 of African descent: they would not be treated gently by Hitler's forces.
Thoughts?