I keep my naughty bits pruned so that stinky bits don't get stuck in it. I can't control it, so I've had the occasional mess in public, and it's not fun. I do all my changing standing up, it's just easier that way, and if you're going to be changing in public restrooms, you might try to master that technic. Of course, as has already been stated, a shower is always the best way to clean up, but not always possible. I use cloth diapers as well, which adds another twist to it. I've got to clean out the diaper as best I can and place the mess into some plastic grocery bags, usually 3, so the smell doesn't overpower, and it's not so visible through the bag. I use paper towels to clean up with initially, then I use some baby wipes or an adult wipe, depending on what I've got in my bag at the time. Then I tie up the plastic bags and toss it into the trash as I leave the restroom.
A tip on keeping the naughty bits bald. I use some hair cutting clippers, electric type, and I just trim real close. I tried shaving before, and the itching is just too much. I've found that I can get it so short with the clippers that it almost looks like I shaved, but it doesn't itch at all. Much better way to do it in my opinion.
I hope that helps.