Don’t put the damp box by heat it will warp and distort.
Bring it inside to a laundry, garage or similar room that is dry and ventilated - if the wood dry’s quickly it will be ruined.
Oxalic acid is used as wood bleach or we have washing Soda crystals Na2CO3 (NOT Caustic!!!) is a strong alkali (don’t use on Aluminium) Either will clean wooden surfaces.
Let the boxes air dry naturally after washing