Like Dave said, and I agree from my experiences. Cozumel has always been a safe port for me.
They depend on the tourist dollar, especially now during re-building. They will ask you to come into their stores etc. But, as far as feeling safe walking around, I do.
Just stay in the tourist areas, and never a problem or even a slight threat of one. Totally comfortable for even a new Cruiser
One thing you will never have to worry about on Cozumel..A taxi back to the ship.