Chartering you own boat with 5 divers is definately the way to go. Thats what we did when we cruised Carnival and docked at the International pier. We dove with Dive With Martin the first time because they were an easy walk from the International pier. It was a great choice!!
We dive with Aldora now, predominately for the big tanks. Keep in mind they offer a 10% cash discount so the 90ish price drops to 80ish which is the same as most 2 tank dives, but with lots of air. Big tanks are a plus for new divers. Chartering your own 6 pack boat may be cheaper...shoot them an email.
As you are shopping for a dive op, the main differences will be cost, tank size, departure point, surface interval location, surface interval snacks provided, number of divers per boat, rental equipment provided, and surface strategy.
Since you are there for one day, convenience would be the biggest issue for me. Unless you know the secret handshake (I don't), getting off the ship can take longer than ever expected. 4000 people or so through one door is going to take a while no matter who you cruise with. If DWM is close, they do include basic rental equipment with their cost. You might see if there is a dock within walking distance of the ship that any other dive ops can pick you up at. Definately chartering you own boat eliminates any time crunches involved with getting off the ship and the boat will be waiting on your arrival. It also lets you decide where to dive (within your skill level).
As far as who? Because of the multiple variables listed above...and variables of variables...each dive op will do something a little different. Finding the perfect dive op for you will take a little trial and error. Aldora works best for us now, but we have dove with DWM and Blue Magic and I can absolutely recommend them without hesitation. I have not dove with Blue XTSea or Tres Pelicanos but they have a large fan base on this site and can recommend them by reputation and glowing reviews on this site. Christi, the owner of Blue XTSea, is a frequent contributor to this site and runs an excellent operation by any definition.
Be warned... a dive in Cozumel is absolutely addictive.
Safe travels, good luck.
Jay