DIY things to do in Grand Cayman and Cozumel for a young family?

[Ancaster]

Hi Everyone,
I hope I'm posting in the right area...
We are total newbies, it's our first Disney Cruise in late January and everyone is excited!

We're a family of 4 (2 adults, 2 small kids).
We love the beach and the girls are probably too small for excursions.
Is it realistic to arrange a beach day ourselves for both stops instead of using the cruise line's "Add Activity"?
(The reason I ask is the only beach day in Cozumel we can all join based on age works out to $290, and our one daughter is not tall enough to enjoy what's included)

Any other fun activities you suggest for little ones?

Thanks!