Not sure where you can horseback ride on those islands and I know there are swims with dolphins in Cozumel and Nassau, so doesn't look good for that either.
A great place to snorkel is in St. Johns, Trunk bay, you can get there from St.
Thomas, beautiful island if you are into snorkeling??
When you get your cruise docs, just check through there at all the excersions on the different islands, sure you will find something good, have fun.
The only swim with dolphins ( outside of Florida) that I know of is in Cozumel and Nassau. There is
horseback riding in Puerto Rico and St. Croix. I don't know what ship you are doing but
check the ship company's web site. They often post there shore excursions there. I think the ships
will offer horseback riding in one or both of these ports.