sad times when "clean" is a subjective term :)
if you have access to lakes and creeks then that's great. But in the drought south west, I have to haul my entire water for 2-3 days.
here are some options, from other BPL threads:
take a squeeze bottle, and make shift a bidet for jet pressure wash.
large zip lock bag full of water with a 3 needle pin holes for a slow drip shower.
If fire is allowed, and no objections to burning nature, you can experiment with the Les Stroud / Survivorman method of White Smoke Bath. start a small fire, than put a juniper bush on it, and kill the fire. To create white smoke. Supposedly that smoke will kill the bacteria. You're supposed to let the white smoke get inside your clothes etc. You may also attract the fire department rescue helicopter...
I wear long sleeves pants and long sleeves breathable shirt and wide brim hat even in the hot summer. so I dont have to use sunblock or insect repellent. my clothes get dirty, but my skin stay fairly clean.
Other question about hair.
There was an entire thread dedicated to our "hair management" that we would never discuss with our closest friends... basically, shave it off... there too, arm pits, shave head, shave beard, crotch, less area to stink up, less area to wash.
but dont shave the night before a trip, you will be itchy itchy itchy, if this is your first time landscaping the gardens. do it a week before, and allow it time to adjust... this may not be for you. I know waxing is not for me.