Got it. So.....a "Box on a Deck" might be of any size or configuration.It's a box on a deck.
When someone posts a 'Deck Box" that sounds very specific to me and frankly never heard of a 'Deck Box'.
Box on a deck (and pic) makes this issue incredibly simple.
The darn thing has a lid on it right? Take any brand (can) of indoor fogger, press the locking top down, open the lid just enough to toss it in and walk away.
Deal with any on the outside as you wish. This isn't hard.