IMO, you need to get the wet boxes open ASAP. The longer you wait the greater the chances of problems.
Yup, leave water pooled and you'll get rust and then mold. The latter can be far worse in the case of media than the former. You can use isopropanol (91% isopropyl alcohol) squirted into tight spaces that you can't easily access to hasten evaporation.
(water+alcohol) evaporates faster than water alone.