I'm surprised no one has mentioned the obvious... bring a plastic water bottle. The thin-walled, small size ones you can crush in your fist to shoot water into your mouth. One or two will fit nicely into your pockets. Demonstrated to me by a very very experienced AN/DP instructor. It's a bit tricky to screw the cap back on without getting salt water in, so think of them as 1-shots.
It's true, you need to be comfortable taking your primary out of your mouth for 10 sec, but that's an OW skill, no?
I generally avoid disposable plastic water bottles, but this is one application that makes sense, IMO. It goes without saying that you must put the empty pod back into your pocket and not leave it underwater.