cruisecritic.com's Ports pages would have lots of info on this.
I believe I've read (on cruisecritic) that the way to do it is through this site:
http://www.resortforaday.com/Westin-Grand-Cayman-Day-Pass-p/gtgcwe.htm
In case yo don't know, the actual beaches in GC are free to be used. Access *can* be stopped, and you can't use loungers/chairs/umbrellas unless you pay the owner of those things, but there are plenty of places to have FREE beach time on the "7" mile beach.