We did six days of diving in Cozumel, and the currents varied from fairly strong to very mild. I don't like strong current much, but there was only one day where it was unpleasant. The rest of the time, you could easily stop and look at something if you wanted to, and there was little to no risk of being separated from your buddy.
Although there are shore diving sites described for Cozumel, I have a feeling that most of them would be disappointing. The terrain underwater seems to be a very shallow shelf that goes out to the walls. Close to shore, there isn't a lot to see (we did two dives off the place we were staying, and although there were a few critters on the seawall, there wasn't a whole lot else). If you get out toward the walls, you're into the current, and may have a great deal of trouble getting back to your entry point.
I think the vast majority of diving on Coz is boat diving. For shore diving, it seems as though Bonaire is more the place.