all the beaches are free .....
a hotel can limit the access to their property but that does not extend all the way down to the water. and plenty of 7 mile beach doesn't have a hotel bordering it.
a lesser know and free beach is found at Smith's Cove, a couple of miles south of the tender landing area. Quite small and used mostly by the local crowd and few cruisers - a taxi wil know where it is. There is a small bath house with a simple shower to rinse and some picnic tables but no food/drinks/music/chairs/rentals. Good snorkeling if you have your own gear.
between here and the tenders is My Bar at Sunset House. It will be open - the hotel dive resort is open and this is the bar and rest' for the resort ... it will be open. Again this is a VERY popular place with the local folks as well as the dive crowd .... been in the same location for a LONG time.
https://cayman.directory/en/yp/my-bar-at-sunset-house-food-beverages-pubs-4380