Not sure if it is still open / offered, but Starfish Island may be an option. It is usually only offered through ship excursions.
You ruled out most of the options in Belize - Mayan Ruins, Caye Caulker, Snorkeling with sharks / stingrays, Cave Tubing, Zip Lines, etc. There aren’t a lot of resorts / beach clubs with day passes near Belize City like there are in Cozumel, Costa Maya, etc.