I'm not sure about Nassau, but definitely not in Castaway Cay. I'm sure it's a liability issue. All of their jet ski (waverunner) rentals are organized guided excursions only.
That was my understanding too when I asked on the boards a few months ago. The jetskis on CC are just for the eco tour(s).
I have no idea about Nassau though because we are on the eastern...haven't researched there (yet)
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