You can have an outside hand washing station at you camp. You can reuse empty liquid laundry soap bottles as a wash station as long as you rinse out the bottle real good to make sure there is no laundry soap left in there.
Then just have a hand towel near you jug of water with a small bottle of liquid soap or bar of soap to assist in washing your hands. This is especially helpful with kids around that always say they wash their hand and you know that they are trying to pull one past you. You will be able to see them wash their hands in front of you now.