Just here to affirm what AnxiousNoMore said - HIV enters through the urethra. It is not possible, no matter what, to get infected with HIV via minor cuts and scrapes that do not require immediate, professional medical attention.
Only the head needs to be covered so you are safe. Otherwise we would all be infected by now if it was as infectious as you are worried - it's a fragile virus instantly dead in air or saliva so the worst that could happen is dead virus touched you.