DH and I use hankies. My nose gets sore if I use tissues. Cotton is softer than tissue paper. They are only disgusting if I have a disgusting cold, which, fortunately, I don't have very often. But I do have perennial rhinitis and seem to need to blow my nose a lot.
Hot wash deals with germs. They go in with towels or sheets that also should have a hot wash.
My mother-in-law used to boil the family's hankies in a pan on the cooker if there was a horrid cold going about. It was, and is, a very healthy and long-lived family.
One could always wear rubber gloves. People deal with dog shit all the time. Do you have a dog, kassi.