You do not need to use different wash clothes. If you are worried about this, you could wash the genital area last if you are using a wash cloth for the entire shower or bath. Soap destroys the lipid layer that surrounds the virus and holds it together. It is safe to touch the genital area for shaving or whatever. You don’t need to worry about spreading it to your hands. Just wash your hands after touching the genital area and you will be just fine. And don’t wash for a long time – a simple soap and water wash is enough.