Most boxes have spansih cedar in them so if your keeping them in those then you will be fine. Spanish cedar is an aid for keeping humidity but if you buy beads then you should be fine in this area as well as long as there is a tight seal in the cooler.
You can go to a local B&M and get some empty boxes usually for free and keep singles in there. Or you can buy some trays to keep those in.
Most work goes with getting the smell out of the cooler and keeping it at the right humidity and proper place to store. No need to fill the whole thing butthats just wasted space
Edit: looks like i just type slow