I don't know why you can't do them on your own, we did and had wonderful operators that took great care of us.
In Belize go to Belize Cruise Excursions
the offer X-Stream Cave tubing and it is a great excursion. Thomas was our guide, great guy and full of info and stories. It is a much better trip then on the ship, we had a group of 9 people, the ship group was aproximately 3 bus loads!!! Take you pick, we got to do extra caves because it was so much easier to keep our small group together. Again, can't compare the prices, we saved about $100 for our group of 4...and we were back with lots of extra time.
In Cozumel we did the furry catamaran and had a great time.
In Cayman we a double excursion, we did the Stingray City Catamaran
and it was incredible, the stingrays are a hoot and the catamaran was wonderful, the North Sound bay is the most beautiful blue you will ever see.
Immidiately after we were pickedup and whisked off to the Honey Suckle Beach Horseback riding
for a ride along the beach on the west side of the island. Amazing!!!
Booking on your own gives you more choices, saves you money and you get better quality excursion, as least thats what I've found. How can anyone offer the same quality of an excursion when you have to service hundreds of people at a time. All the trips we did had 8-20 people!!