How can I avoid being charged/arrested for public skinny dipping/nudity?

Sorry, none of this is going to work. You won't be able to get permission from either the pool owner or the police. And when the police come to arrest you they aren't going to listen to any of these rationalizations or excuses. They are going to take all of you to the police station and then call your parents. Sounds like a bunch of kids planning a very stupid stunt.