I am a travel agent/cruise specialist and when my clients ask these questions, I usually check with the tourism and visitor's bureau in their destination. Most of the ports throughout the Caribbean have really good websites and are easy to find on a search engine. The bureau usually has the latest, most reliable information on approved companies for island tours, using taxis. But, be very sure to get back to the ship in plenty of time before the ship leaves - they make an announcement on the ships, so listen for the message and maybe even ask the security personnel as you disembark for the port.
Please feel free to e-mail me if you have any questions!