Sounds like he's an older juvenile to adult snake in decent shape - you really don't have to worry too much at all about the stress for him to remove him for cleaning for a couple of hours. Young snakes get shipped in many cases, which is far more stressful. Put him in a tub with holes and clean away. Do it at a timing that's convenient for you, it's not that big of a deal. What is important is doing it ASAP though - being in a dirty home is far worse for him. All at once is definitely better than piece by piece. Using diluted bleach is a good option here - just make sure to rinse until bleach fumes are gone if you do.