Take one of the ship's excursions to Stingray City. Book a morning excursion.
When your are returned to town, walk along the shore road to the Eden Rock Dive Shop. You can snorkel behind the dive shop. It is "iron shore" but there's a ladder installed for easy entry to the water.

Another option after the Stingray City excursion is to take a taxi to the Cemetery Reef beach. It's about a 10 min. ride. You can arrange for the taxi to pick you up in a couple of hours. There's a nice reef about 300 yards off that beach.