I would definitely not bathe an ill pig with a URI, that seems like a bad idea!
I typically use either Bunny Bath or I buy a brand called "Earthbath" that's designed for dogs but is organic (and has oatmeal and aloe to help with their skin. I would just make sure there are no pesticides in it (so no flea shampoos) and that you get a gentle formula without a lot of perfumes.
We are as gods to the beasts of the fields. We order the time o' their birth and the time o' their death. Between times, we ha' a duty. - Terry Pratchett.
"Men have forgotten this truth", said the fox, "But you must not forget it. You become responsible, forever, for what you have tamed. - Antoine de Saint-Exupéry