Yes, the dry air will do it. Humidity I would say should be 40% or higher, within reason. I mean you don't want it to be Amazonian style jungle in your setup.
I'm not sure what is available in your area, but a good hygrometer might be a worthwhile investment. I've actually heard cigar shops have some really nice options because of the interest in keeping cigars at a certain humidity, and they're usually pretty small too.