I'd be worried about itch too. Would never shave my under arms.
I've had my chest waxed quite a few times. Never had to do my back, as I don't have a hairy back. But my chest and stomach hair is a veritable force.
Also generally clipper my pubes, and used to clipper my face, and just shave my neck. But then decided that the neck is the worst part anyway, so I just razor the lot, probably twice per week. But my facial hair is black and grows really fast, so comes back really fast.