That depends on which cruise you are on. Dive with Martin is at the end of the International pier and is a 1 block walk from Puerto Maya. We cruised on Carnival and docked at Maya and walked to DWM in about 10 minutes or less. All dive ops will work with you to accommodate your needs. The problem with cruise ships is most morning dives leave at 8:00 am. Most ships come in on their schedule, then it takes at least 45 minutes to get off the boat.
what we did was email the operator of your choice...start with 4 or 5 and let them know your schedule, your experience level, how many divers, any special needs ( I need BIG tanks) and anything in particular you want to do. my wife and daughters were with me so we had 4 divers, it was only $40 more to charter our own boat. We walked to DWM, out boat was waiting, and we were off to the site within 10 minutes of getting there. Dive was great, limited the depth to 60 feet because of my 14 year old diver, but we were on the bottom and saw lots of fish, coral, turtles, eels, etc.
you can't swing a dead cat in Cozumel and not hit a dive operator. Everyone has their favorite, and there are very very few wrong answers. dive With Martin has been around forever, and depending on which port you come into, may be the closest. I have dove with Blue Magic and loved them. They have the best sleep and dive rates...but that doesn't matter if you are cruising. blue XTSea is run by a member of this forum and I believe their website has a special link for cruise ship divers. Christy frequently contributes and is a great source on Coz information. I have never dove with them, but they deserve a look. Aldora, Blue Angel, Tres Pelicanos, and probably 100 others are great operators that will work for your business. I would not worry about being picked up at the pier, cabs are cheap, safe, and always available to get you where you need to go.
the biggest issue your going to have is scheduling, so start emailing dive ops now. Also check out the operator the cruiselines uses very well. Trip Advisor probably has lots of reviews. That convinced me not to go with the cruise line operator. Crappy equipment, uncaring staff, and poorly run operation were current complaints.
The threat of being left if your late if you don't use the cruise operator is overblown. Your going on a 2 tank dive with 90% of the site within 30 minutes of the pier. We saved a little money and had our own boat by finding our own operator and made it back from diving with more than enough time to take our gear back to the room, shop, have a few beverages, eat, and be back on board in time to watch the "drunk pier crawl" of hammer drunk cruisers trying to get back to the boat. (One of the best parts of cruising)
email the op of your choice now, pick the one that works for you, pack your anti fog, and have fun!!
safe travels
jay