We just got back from Cozumel last month. I wouldn't stay on the ship as there is a lot to do and see there. Have you looked at your shore excursions yet? Did anything catch your eye? You don't necessarly need to book through the cruise ship, but it will give you ideas of things people enjoy doing while there.
The beaches there are beautiful, and you can easily take a taxi there and back. Most people can't sit at the beach all day, so you can relax, get there when you get there and leave in time to do a little shopping then get onto the ship.
If you're going to Tulum, Xel-ha, or X-Caret (these are on the main land), you will probably want to do the ship excursion so that you have priority getting off the ship and will be back in Cozumel in plenty of time to catch the tender back to the ship.
Don't let a little inconvenience distract you from the good times to be had there