With a compromised imune system, fighting off a skin infection is not easy to do in the back country. This is not the "normal" for most. The medications you take are shutting down the normal imune response from your body. Soo, even the normal bodily bacteria that help keep you "clean" are posing a danger. Be very carefull with food spoilage (not necessarily botulina.)
If you weekend routines work, then simply extend those between watering holes and wash thuroughly when you have a lot of water available.
Your hair is, perhaps, the dirtiest spot on your body. Open to the air, it collects bacteria, sweat, spores, pollen, dust, bodily oils, urea, etc making it a real breeding ground for bacteria. Even your groin is not THAT dirty, well, at least it is not normally open to air. Wash with water every day. Or, as was suggested, shave your head or use a very short hair cut. Long hair is good for avoiding bugs, but with a suppressed imune system you risk infection. Again, water will get it cleaner than soap and water the next day. Try to do your hair first, using about half the water you will be washing with. Again, wet your hair, dry with a bandana, wring it out, wet the bandana and wring it out, repeat.
Soap is quite difficult to totally wash away. While it removes a good percetage of dead skin, bacteria and fungi, it will usually be more difficult to remove, also. It can act as a food supply for the bacteria that are left, bringing about higher concentrations of bacteria, et al, on your skin. You really need a LOT of water to clear it from your body. Like a shower or lake/stream immersion. If you cannot do that do not use soap. Just wipe down with water two or three times. You will actually be cleaner the next day. Just use a pot of water, pour water out to wet your bandana (cotton or linen,) wipe down, wring it out, add water to wet it, wring it out, repeat untill you are done. Be carefull with "wild" water, guardia, crypto, etc can enter you body through body cavities or nicks, scratches, bug bites & cuts...any injury that breaks the skin. I would suggest you boil a pot before washing...either on the stove or on a fire.
Usually baby wipes are glycols, lanolin and a series of preservatives that were not approved for consumption, though some may be. Preservatives usually reduce or stop bacterial growth. Despite adding food (lanolin is an oil, glycols are sugar based) to your skin, they often inhibit bacterial growth for 10 minutes or so...some much longer. However, I have seen a few recomendations for drying these out for hiking. This is not really possible with a lot of the esters and other stuff that cause the antibacterial actions. A lot of the chemical soup just evaporates off. Along with any perfumes.
Avoid anti-perspirants, and anything that will slow down sweating. One way to clean up is to wipe down your "sweaty" skin, wet and wring out the bandana and repeat. Sweat wettened skin will help wash your body. Let it do its job.
OK. You have gone through about a half quart of water washing up. This should hold you till the next day. When hiking, your feet are important. Get a shoe that is large enough to wear two pair of heavy socks. You might need only one when hiking, though. When you are done with all the clean-up, do your feet. Your feet may get a blister or two. Keep you nails trimmed. Pop and sterilize any blisters, then cover them with duct tape after a complete drying. Usually this will last for two or three days...enough time to start the healing process. Larger blisters can be covered with a layer of superglue, first. And/or squirt some under the blister and press/wipe quickly with your fingers. Yes, your fingers will get coated, too. WG will double as a sterilizing agent if you don't have alcohol (at least 40%...scotch, bourben, vodka, or other alcohol works well.)