There's a moral to this story, always carry a clean up pack
I have UC and can identify all your concerns, there's a saying in the British Army any fool can rough it, so I hardly ever go out without my pack which contains toilet paper, spare pants (underwear) kept in a sealable plastic sandwich bag, which prevents them getting wet if it's pouring with rain or I fall into a river etc. also comes in handy if the worst happens and you need to store your unclean underwear in a sealed bag, which prevents smells escaping, baby wipes to help clean me up just in case but also to clean that public toilet seat including flushing handle if I am fortunate enough to have sufficient time, bottle of water, and finally a lightweight camping towel which again I store in a plastic sealable sandwich bag.
All the items take up a small amount of room in a small rucksack so I still have room to keep any small items of shopping I may want to buy.
Preparation prevents poor performance, and carrying those items instills confidence that you can always sort yourself out if the need arises.