Sounds like too much fiddling (and too much water-adding). If the cooler has a good seal, then you only have to add a very little water - just to replace the moisture lost each time you open up the cooler - and very little moisture will be lost if you open up to an ambient 60%RH.

If you find yourself always opening the cooler just to check RH, just pick up a remote temperature/humidity weather unit, say from Oregon Scientific. They are pretty inexpensive, and some can handle multiple channels. IIRC, mine was $40 on eBay or Amazon. Once you look at the display a few hundred times, you'll stop looking at it ;-).