I don't clean the wood box. Like others, I cover the top of the wood box before the smoke with AL foil. When I am done smoking, I pull the smoke box out (with mittens!), place it on a couple of bricks, pour water over the top and inside the box on the left-over wood/ash to extinguish. When the box cools a bit, I remove the foil from the top and the left-over wood. Then one more rinse of water through the box, and it goes back into the smoker for the next time.
In terms of cleaning, the AL foil on top of the wood box gets all of the drippings, so when I peal that off, the top of the box is basically clean.