It’s possible to drop change into someone’s hands without physically touching them though. I don’t like physical contact either, and on the rare times I pay with cash, I hand it to the cashier without making physical contact.
I remember there was one store I went to that the cashier literally put the change on the counter right beside my outstretched hand and open palm, every time. And it was annoying to pick up change from a stainless steel counter. I know I was being petty, but when I noticed the pattern, I started putting change on the counter (if I paid with coins) when paying so she could experience having to pick up coins one by one from a stainless steel surface.