I have done this route from ft Myers FL half a dozen times. As the other indicated by sailing the most natural route i.e along the cuban then puerto rico
coast you will be heading into the wind
most of the time and will make very little headway tacking. Ft Myers St Thomas takes me about 10 days with one stop in Puerto Rico
for refuelling but I have to motor
sail most of the time.
You may try a less taxing route as I will do in January since I will not be in a hurry. Cross over to the Bahamas
sail through the Bahamas
bank then Nassau
and work you way down through the Exuma.all the way to Turk and Caico. Then hop over to San Juan
PR . From there you may sail to St Thomas.