If it were me, I'd document. If you are in the Bahamas
I think you can find a company in the US who will do all of the paperwork for you. When we bought our boat in Florida
we had such a company do all of the titling and transfer the documentation. I think we paid about $400 for everything. If you have never been documented I don't know how hard it is but the CG website is pretty good and if you have to call the folks in West Virginia, I found them very polite and helpful!
But, you are likely to run into some officials who will be much more comfortable with USCG registration. The Turks and Caicos
are fairly strict about importing and exporting but I found the officials in Provo very nice, if difficult to get ahold of. The DR will want to see a lot of papers when you enter and then will track your trip with despachos at every port. It is also useful to get a Customs
decal for US ports
. You can get it for $10 online. It makes it a bit easier if you sail from place to place in PR and the USVI.
There's my two cents.