I haven't been from the cruise ships, but pretty much all of the dive sites within reach of a day trip in Cozumel are in the park (although I thinks it's Chankanaab). The new cruise ship dock isn't all that far from the dive spots (the old dock is pretty far). I would just book through Disney - it's much easier and they guarantee the ship won't leave without you.
Cozumel diving is beautiful although it is "drift" diving. This means you don't start in one place and swim back to the boat. Instead you drift along with the current and the boat swoops in and picks you up when you surface. Works pretty good unless the current is doing weird things (one time the current was heading south on one side of the reef and north on the other - so the divers were spread over a 4-mile swath - took almost 25 minutes to get picked up).
Beach diving is limited as beaches are pretty limited. Most of the coast is very narrow rocky beaches. Any "beach" area has been planted there by the resort owning the beach. The current is also an issue with beach diving. If you beach dive, you will end up far from where you started and have to walk back.
If you want a beach/bar experience for you and diving for DH, you might try the Presidente hotel. They have a swim-up bar, beach, etc. and also offer diving (they have dive packages).
Have your DH PM me if he wants more info.
Sweet Sue