This is my shower set up. Just hand wash.
If out doing stealth camping, the metal cup, dawn dish detergent, mini water bottle and hand towel is what I use.
Basically if it is hot I can skip the cup and just use the water bottle (only pure water inside), and squirter my head a tiny bit, put a dab of dawn on it, massage it in, hit my stinky parts with the foam.... then squirter it away. Then I use the hand towel to dry off. I stand on my shoes while doing this, then get dressed, and sit on a log and do my feet. Then I hand twist the towel to help dry it or hand it up in a sunny patch. If cold I heat some water in the cup, and pour a small bit into the half filled bottle (they will melt if all hot water). Squirt squirt, hot shower. The dawn dish soap has many of the same ingredients as laundry detergent so can be used for laundry as well. And the smell is common, associated with houses. So people don't question it.