Based on over 1000 nights camping over the past 10 years, here are my observations about keeping clean:
1) Stretch your muscles so you can squat properly, which positions the body so that there isn't so much mess in the first place, then wash your bottom with water after wiping. Then clean the hand you used to wash your bottom with soap and water. Yes, this wastes some precious water, but it solves the biggest single issue with cleanliness outdoors. I wipe with natural objects (rocks, sticks that have been smoothed by rubbing against rocks, sturdy leaves), which work much better than paper when it is raining. Wet wipes is another possibility, but is one more consumable that can run out and which has to replenished at town stops, with the potential for out-of-stock situations, which is why I prefer my system, which is always available.
2) Wear loose-fitting nylon shirt and pants against the skin, with no underwear for men. (I can't comment about women's underwear.) Nylon (aka polyamide) is highly stink-resistant to begin with, cleans easily in hot or cold water, and dries quickly after cleaning. Supplex nylon breathes very well, just like cotton. Polyester and polypropylene are stink-magnets. Wool is also stink-resistant (though has a smell of its own when wet) but is slow to dry and isn't very durable. Then wear insulating garments on top of the loose-fitting nylon, so that they are protected from contamination.
3) Wear wool or wool/nylon blend socks stink much less than polyester socks and are easier to clean (cold water and shampoo will clean wool, whereas hot water and strong soap is often needed for polyester).
4) Clean the feet in the evening by scraping them in dry dirt. Yes, you read right. Dry dirt is mostly just fine sand and even the organic matter is less-smelly than the bacteria and fungus that collect on the feet. Even wet dirt can be used to clean the feet. Just brush most of it off aftewards, then keep the feet elevated for a minute or so, which should be enough for the remaining dirt to dry, then brush that off. Cleaning the feet is essential to keeping the sleep gear clean. Truly bad foot smell will go right through a silk liner.
5) Wear wool or fur felt hats, since the head is full of oils that can go rancid and smell. Wool and fur will absorb these oils (which are similar to the oils that were on the wool or fur originally) without smelling bad.
6) A towel is unneeded and will mildew. Just put on the loosely-fitting nylon shell clothes and burn off the moisture with body heat.
7) If hot weather, rinsing salt off the face might be advisable in the evening, since salt deposits can burn the skin.
8) Underarms will tend to stink far more in cold weather than hot weather (assuming you are wearing loose-fitting nylon) because lack of air circulation there under cold weather clothes creates a hot and damp environment for bacteria build-up. It's a simple matter to strip down and clean with soap and water, assuming you have the right soap and water bottles. Practice at home. The human body won't be hurt by being splashed with a little cold water, even if air temperatures are near freezing, as long as you can put warm clothes on afterwards.
9) I recommend using shampoo with conditioner inside a 4oz Nalgene screw-top bottle as your soap. These Nalgene bottles are sturdy and the wide mouth allows inserting a finger so as to remove just a tiny bit of soap. Shampoo is gentle soap and the conditioner reduces the likelihood of drying out the skin, regardless of which part of the body you are washing. Shampoo with conditioner works fine to clean both supplex nylon and wool in the sink.
10) Evening tick inspection is advisable in many areas. Less of an issue for bicyclists than hikers.