Understand two things first. The filters are to be kept DAMP, not saturated.. So, there is not a lot of water in there in the first place. I expect that they would dry out (in a normal interior climate) before the 'grew' in any case - much as the sponge on your tip-cleaner if you use that method. Second, any filter you use will either need to be cleaned or replaced with some frequency depending on use.

With that in mind, synthetic filters are not attacked by most common solvents and disinfectants. So, one tablespoon of household bleach per pint of water, a 10% solution of isopropyl alcohol and water, two jiggers of vodka per pint of water, a teaspoon of borax per pint of water and so on all would take care of any growth issues.

Peter Wieck
Melrose Park, PA