My favorite is the following (5 years active in the Marines, so we love to rip on the Navy just as much as they love to rip on us). This one kind of depends on setting it up right and eliciting the right response from the person you tell it to for it to work correctly.

You: So, did you know that the Navy invented sex? Other person: Wait what? (or some sort of response like that). You: It's true. But the Marines introduced it to women.

I wonder where that originated because I've always heard it as a state a/b school system or college a/b joke

Seriously though, if you're going pee whether it's in public or at home, it's not a bad idea to wash your hands. That being said, I really don't see it as necessary because unless you're literally pissing on your hands, the worst thing you're going to touch is the toilet handle with like a finger and unless you have herpes or something your dick is just skin like the rest of your body. What I'm getting at is that depending on the situation I may or may not wash my hands after peeing, and if I don't it's a conscious decision and I don't want any god damn grief about it.