Does your town or community HOA have anything in writing regarding "quiet time"? As long as you obey these, I would think you'd be fine. Washing a car can't possibly be noisy enough to annoy neighbors, unless you're doing it with your grill wire brush.
Others made good suggestions - talk to your neighbors, make friends, explain your situation/work schedule and why you want to wash during those hours. Bribe them with a box of donuts if you have to as a "Nice to meet you, I'm new here" kind of an ice breaker. My guess is any reasonable person would be OK with this, unless you're dealing with an elderly person who thinks you're disturbing their peace, even if they're hard of hearing.