There are a couple of different ways to wash your hands there. The first one is having a small bottle of hand sanitizer with you (my wife always has one without fail) and using that. But, if running water is essential then I would suggest putting the swimsuit back on and taking a walk over to Kontiki (which is sort of close by). They have restrooms with running water, as does the Bikini Beach Bar. As a thank you, I usually buy a beer or a mixed drink at the bar to give them some business. Of course, there's always taking a dip and washing your hands in the salt water of the ocean. These beat going back to your condo or hotel room and washing up (which I suppose is a fourth alternative).