Parents + kids 8 and 10 years old. Don't want to spend money (as little as possible). Don't need drinks or water toys or attendants or lounge chairs or anything an "all-inclusive" place would offer. DO require a nice little beach plus good snorkeling.
Ideal: this happened in St. Lucia. I assume Cozumel is too developed for it to happen there......but as a guide for what we are looking for. A gentleman had his own boat pulled up by the cruise ship dock. He took me & wife to a secluded cove where we were by ourselves for several hours on a deserted half-moon beach, between two hills. 50 feet offshore was a coral reef with amazing snorkeling. He came & picked us up in time for the ship. Total R/T: $30.
I know nothing like that is likely to happen in Cozumel...but what would be the best non-ship-crushed beach to lie around & snorkel for free?
Given the tropical heat and sun, you and the kids will have a much better time at a beach club where you can get a shady palapa and access to restrooms, food and cold drinks as opposed to a deserted beach.
No snorkeling, but here was our solution, which was great:
VISIT THE EASTERN SIDE OF THE ISLAND. My god, it is beautiful over there. And wayyyyyyyyy more deserted. Miles and miles of beautiful rock formations going to the sea, with the occasional pretty beach. On the land side...scrub, just scrub, MILES of scrub, with no development at all. WILD. I never knew part of Cozumel was wild. It was so pretty.
So the first thing we did was rent a car and drive the entire circle. We stopped and looked at the west side resorts, then saw the east side. I wanted to just stay on the east side after lunch, but kids wanted to visit Paradise Beach with the bouncy toys in the water. Mistake...more later. We lunched in San Miguel (Americanized Mexican at some nameless place, but my fish tacos were very good). Then on to Paradise Beach.
What mass-marketed pablum Paradise Beach is. Absolutely no snorkeling in the area (though they say snorkeling on their website). Literally thousands of people. Paid $20 for a bottle of sunscreen (stupid me forgot ours) and $12 for each of my kids' wristband to climb on the toys. By and large, though, the toys are designed for athletic teenagers to get on...smaller kids or fatter old people have about as much shot at winning the lottery as climbing their "ice mountain". We all hated it and left in less than an hour.
And went to the east side, where we found an actual beach, with ACTUAL SURF (lovvvvvvvvved it, me & son spent an hour body-surfing) and we. Were. Completely. Alone. ALONE. On a beautiful beach. On a hot day. It was amazing.
On the east side, there are plenty of beautiful deserted beaches.
Programs: DL-Platinum; Hilton Diamond; Marriott Gold; National Executive Selection;
If you are divers the Eastern coast is great. The surf is too rough there for good snorkeling.
For children I would use caution as the surf is very strong on that side and there is severe undertow in some areas...swim there with caution...
There are a few good snorkeling spots on the Western coast, but unfortunately they are in front of either Chankanaab Park (a National Park with a great snorkeling area, a separate cove for swimming, a dolphin encounter, etc. The area near the Presidente Intercontinental hotel has wonderful snorkeling but I'm not sure how you can access it without being a hotel guest.
The cozumelinsider.com website has more info on Cozumel beaches and which are best for what interests you.
Your idea sounds idyllic though and I hope you find someone to take you there!
Just as a side note, if your Western Caribbean cruise happens to take you also to Grand Cayman, you could come closer to this experience there I think if you hired Captain Morgan to take you to Cayman Kai on the North Point of the island.