Depending on how detailed you want to get and how much effort you want to put in it, disassembling the box is best but a ton of work. When I get a used box, we wait for a sunny day, roll it outside and wash it with car wash soap in warm water then pressure wash it off.(without disassembling it) Course my main business is pressure washers so that is easy for me. A garden hose will work also. Then I wash the insides of the drawers too. The take a blow gun, and blow the majority of water out of the drawers and pay careful attention to blowing water out of the slides. The with the drawers partially open, let it dry. In the winter, I'll use the torpedo heater to dry them. I wash the drawer liners with a degreaser on a flat surface and hang them up to dry. If you are concerned about water laying in the bottom of the box, you can remove the bottom drawer and wipe the bottom dry, I normally do.
As long as you get the box and slides dry, you will have no problem.
Good luck!!