If I were to skip a port it would hands down be Falmouth, there is a reason Disney skips Falmouth for the Star Wars Day at Sea as opposed to Grand Cayman. The shopping at the Falmouth port is exactly the same shops that will be in the port at Cozumel and will be repeated again in Georgetown and downtown Cozumel.
If you like to snorkel there is a lot of good snorkeling from the shore. You can rent gear from Eden Dive Shop, which has good snorkeling right out their door. If you like the Beach, they have miles of awesome beaches and resorts. The downtown shopping is also nice and probably the most pleasant in the Caribbean as far as pushiness goes.
I know a lot of people that have done Stingway City and they've all loved it. I've also heard good things about the Turtle farm.
The island is also very safe, so there is no issue at all with going out on your own. I've ridden the local buses ($2pp, make sure you have small bills they don't have US change), gone off to a secluded part of 7-mile beach, walked all over Georgetown and never felt unsafe at all (meanwhile, I will not leave the port in Falmouth unless I am with a tour operator).
Tendering can be a little bit a hassle, but I also think it is fun and not that big of a deal.
Edit: Eden Dive Shop is less than 1/2 mile walk from where the tenders drop you off. There are some other good snorkel spots a 1/2 to 1 mile walk the other direction from the tenders. So it is easy do some decent snorkeling without paying to go anywhere.