I think that's why Dogbowl suggested trying to make arrangements with a local operator (see below) rather than a cruise ship excursion, but it can be difficult due to the timing. Grand Cayman doesn't have a cruise ship pier and passengers are tendered into port, so it probably takes a little time.
If you meet a dive buddy on the boat you could share a taxi to Turtle Reef and Macabucca to do a very nice shore dive (or two) for only about $15 CI for a tank and weights and have a good lunch right there when or between dives. Are you bringing the rest of your gear with you? I don't recommend the Eden Rock and Devil's Grotto shore dive that is very near the harbor. It has been beaten up a lot, but there is a lot of fish life and if you are going during the Spring, you might be able to catch the bloom of the Silversides.
Cozumel has a huge cruise ship pier - they may have 2 of them?! - so might be able to get off the ship quicker and hook up with a local dive op, I don't know.
I don't have experience with cruise ship dive excursions, but I have heard that they can be very expensive and don't always take you to the best spots - but I'm sure that they will get you back to the boat on time.
