I would go with Moomans suggestion.

I am very wary about using any form of oil on the skin of a bodhran. If you get it wrong that will mean you end up with a slack skin, permanently.

I have only one non tunable drum now for the simple reason that the humidity here varies non only seasonaly but by the day too. Anything from 30% to 90%.

Even tunable drums need drying out so I slacken off the tensioning nuts and put them under the air-con when it is on a cool and de humidifying cycle. The dryer cool air will help remove moisture from the skin. Mine are fairly thick skinned {please no comments about thick skinned bodhran players ;-)} Otherwise believe it or not pop them in the fridge. Cool air will help dry them out, the alternative is the hair dryer on warm to evaporate the mositure out of the skin.