It is what goes in to the water from your washing that could be polluting.
If wild camping you want to be washing etc away from any water source. Also you want it to be minimal weight as you have to carry it in and any waste gets carried out. Even wet wipes have weight.
When wild camping in Scotland or the Lake District which is where I usually go I just take a bar of natural soap and find a lake to swim in. The soap I use is just basically animal fat and oatmeal (no shea butter or palm oil). I love wild swimming when camping, very refreshing and invigorating.
I know the post is 5 months old. There is already products which fits the bill, described for the survey, for washing. No water needed or wet wipes. I have used it for my wild camps.
------------- New Year: Hesketh Bank
Feb/March: Red Squirrel
March: lakes
June: Morecambe
Aug: Lake District(not camping camping)
October: Red Squirrel
Just done a week in Scotland & my MO didn't vary from any other cooler weather multiday trip. A midweek going over with a wet wipe & footpowder to the nethers a couple of times. My baselayer stayed on my back night & day as it was dry. It's treated with polygiene so didn't smell much. I wore the same socks (smartwool) & undercrackers (Saxx Quest) all week during the day. For a weekend I wouldn't bother. In warmer weather I'm not adverse to a dip but wouldn't wash in a lake or stream.
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.