This is fine if you want to emphasize who is doing the action, for example: "Who looks after granddad?" "No-one! He washes himself." Or, as Pia says, "children have to learn to wash themselves." However, if you just want to describe the everyday activity, you would say, "This morning I got up, I got washed and I had a shave." If someone asked, "What happened to granddad's beard?", you could say, "I shaved granddad" but, if you're just talking about something you did today, you'd say, "I gave granddad a shave."

What about shave?

No, children have to learn to wash themselves