As long as he's been eating regularly for you, it's definitely okay to switch him! The most important thing to consider is his size. I generally like to give my snakes enough room to stretch out 3/4 of their body length in a tub, but I know others do it differently. I would also still provide him with hides at least at first since he'll have to adjust all over again.

But it's amazing how much easier tubs are to maintain compared to tanks, and much nicer to move around and transport as well. I used to keep my first bp in a tank too until I came to the same realization, and now I would never go back to tanks! (for most snakes at least)

And yes, I would definitely wait until he's done shedding to switch him over. If it's already been a week then it should only be a few more days