Take the taxi service on your own. The prices are reasonable and there is no dishonesty in Cozumel. We took a taxi to Ocean Club, a new beach side resort, and it was fantastic! The fresh water pool was the most refreshing since all the pools on the ship were salt water. The food / beer was cheap and good!
Then we took another taxi to downtown for shopping and this was great too. Just be prepared for a lot of walking. All prices are negotiable so don't be scared off by sticker shock.