While I usually wash my hands after a restroom visit, I think its mostly a feelgood thing to do rather than useful in terms of hygeine. Think about what you do when you wash your hands: 1. dirty hands: open the faucet. 2. rinse/soap/rinse. Hands now clean. 3. close faucet...WAIT A MINUTE- that's the same faucet you just touched with dirty hands. So you just "undid" your handwashing. 4. Grab a towel (many restrooms have manually activiated towel dispenser, so another dirty contact point. So unless the towels have hand sanitizer on them (nearly all do not), you've really done nothing. 5. open restroom door and waslk out. Well there goes another dirty contact.
Obviously, you haven't mastered the use of the side of your hands/wrist as well as effective paper towel management.
Turn off the water with either the side of your hand or using a paper towel. Dispose of the paper towel post turning off water and opening the door to the restroom.
Beauty is truth; truth beauty - that is all ye need to know on earth...except TCP/IP.