I've done the same thing a few times, too. Here's what's worked best for me:
1. Get recommendations for a few dive operators from SB members in these forums.
2. Check out the operators' websites for information about prices, boats, rental gear, dive sites, accomodations to pick up cruise ship divers. This helps me to narrow down the list a bit more.
3. Email the operators I'm interested in telling them what dates/times I will be on island and what I want to do (2-tank morning dive, 1 tank afternoon dive, etc). If I can't find the info on their websites, I ask the operators if they have nitrox available and the cost, boat safety features, can I dive the limits of my computer or am I time restricted and especially
will the operator get me back to the cruise dock on time?
4. Sign up with the operator whose responses seem best to me.
I recommend
Aqua Safari for diving Cozumel. Their staff is as attentive as you want them to be. I prefer to be the only one who touches my gear and they respect my wishes. But they'll set up your gear for you if you want. Because Coz is drift diving, there will be a DM in the water with you and you are expected to stay within eyesight of the group. The viz is usually wonderful, so that's not generally a problem. You will want to stay close to the DM anyway because of all the interesting things he will find for you. The boats are in good shape, comfortable, safe and have mask and camera rinse buckets. Snacks and soft-drinks are served between dives. One of the crew is always moving among the divers serving cups of bottled water. Most of their staff has been with them for years, which says a lot in such a revolving-door business. They are also reasonably priced.
Good luck and dive safe!