A propane furnace (with a heat exchanger) will produce equally as dry heat as an electric heater, since both just take the air from inside and warm it up without changing the amount of water vapor in it.
If it's the noise of the furnace cycling that is objectionable to you, perhaps it would be worth considering a hydronic (hot water) heating system. The pumps and radiators can be pretty close to silent, and you might be able to run it off of the existing water heater for the shower and sinks. This would likely not be a typical factory option for most travel trailers.