Russia was not getting anything which could be called an "invasion fleet" out of the Baltic Sea, Black Sea, Arctic, or Far East which could even threaten Martinique back then so if the US gave Martinique to the Poles the only real threat they would have faced would have been France or Britain picking a fight while the US was distracted: see: The French involvment in Mexico during the early 1860s.
In that case,they would gave it up later,becouse public opinion was important and picking on last refuge of Poland would not sell well.Which lead to polish island after 1918,and polish goverment there after 1945.
Maybe with what was left of our fleet from 1939/by that time,it would be 2 destroyers/
And, in 1989 our goverment could come back to Poland.
P.S polish soldiers could again be mercaneries - against all soviet coups in third world countries.Maybe they would save Ethiopia or Nicaragua from becoming soviet puppets?
Even if not,they still come back and modernize polish army.