I believe that tranfer of colonies between powers was allowed according to the (original) monroe doctrine.
The standard work on the "no transfer" principle is John A. Logan, Jr.,
No Transfer: An American Security Principle (New Haven, Connecticut: Yale University Press, 1961). Unfortunately I don't have it with me now, and my soc.history.what-if post summarizing it is no longer available (thanks, Google!) but a few things I do recall about it: (1) The principle actually antedated the Monroe Doctrine--for example in the early Republic there was always concern that a weak Spain might sell some of her New World possessions (above all, Cuba) to a strong Britain; (2) the principle was eventually associated by most Americans with the Doctrine, though Monroe never mentioned it in his famous 1823 message (IIRC, Seward was the first Secretary of State to explicitly link them) and (3) the US did not consistently try to enforce the principle; it did not, for example, object when Sweden gave St. Barthélemy back to France in 1878.
With regard to the Danish West Indies, the US was interested in them as far back as the 1860's and especially after it began work in an isthmian canal, it would probably object to Denmark's selling the islands to any stronger power (even Italy was stronger than Denmark)...