We were on the Western on 6-22 and did our own. It was very easy and a lot less expensive.There were 5 of us, DH,self, DS's-12-12-8. We have our own snorkel gear, about $20 at Wal-Mart, Target, and Costco.
On Cayman, after tendering to the dock, there were cab drivers waiting in line. I think it was $3 each plus tip.You will want to go to seven mile beach. All the beaches are public, but the chairs are reserved for guests of the resorts. My parents went to the Holiday Inn and said it was great. We went to the Marriot at the suggestion of the cab driver. We ended up walking three resorts towards the ship and putting our stuff on a brick wall on the beach. Swam right out and saw some great fish of various types and lots of coral. You will need to swim out a little until you reach rocks and coral, because that is where the fish are. We snorkeled for about two hours and then decided to go back to the ship. since we were on our own, we did not have to wait for anyone.
We walked back, but it was a little bit of a hike in the heat. You could catch a cab at any of the resorts. We tendered back to the boat, left the eqip in the cabin, rinsed off at the pool to cool down. We hit Pluto's for a quick lunch, and left the kids on board with my sister so that DH and I could shop for Rum Cakes and Rum. Very easy. Cost of excursion for five: $17 cab ride with tip.
Cozumel was even easier. Chanaknaab Park.(sp)Go to the cab line to the left when you get off the pier. Ignore the vendors trying to sell you excursions. Take a $10 cab to Chankanaab Park(up to 4 people). Admission at the gate is $10pp,children 7 and under free. Once inside, follow the maps to the beach and go towards the end were there are less people. There are plenty of chairs and some shady palm trees (earlier the better). There are steps cut into the sea wall to get into the water. The best snorkeling is close to the wall and reefs. There were almost as many fish as Cayman. After snorkeling, you can explore the park and see Iguanas, Indian relics (some fake), and get a snack or beverage at the many stands. If you explore the jungle, you may want bug spray. There is a dolphin swim, but we did not look into it. There is also a performing dolphin/seal show for an additional fee. When you are done exploring, walk to the main entrance and a cab will be lined up to take you back for $10. After dropping equipment in the room, we ate a snack and went into Cozumel to shop.Cost of excursion for five:$64 (they let in 8yo for free)
Enjoy your cruise-whatever you decide.