I've taken many St. Thomas taxis and have lived to tell about it. Sometimes, you have private taxis, but many are vans or even bigger trucks with covered seating in the back (it's not as bad as I've made it sound, it's actually quite comfortable). Usually there are a line of taxis on the pier, and sometimes the driver will wait a bit to fill up with people going to the same place. This is especially true for taxis going to downtown, Magens Bay and the Red Hook ferry.
I'd say just grab a taxi to the beach. This way you're on your own schedule, not the excursion's. Many drivers will arrange a time to come pick you up, but finding a taxi is never a problem.