Crazy, I would highly advise you NOT TO rent mopeds, scooters, motorcycles, or the like, in Cozumel. The roads are in SEVERE disrepair. And, by disrepair I mean big pot holes and large, broken pieces of asphalt/pavement lying in the road, etc.
You will need to devote your full, undivided attention to the road. You would not be able to look away for even a split second. It's that bad.
Cozumel residents drive crazy too. You'll have your hands completely full trying to control the moped, watching for signs, and being on the defensive with Cozumel drivers. I'm sure others on this forum would concur with me.