On the furnace, are you talking about a single click when it the furnace comes on or a repetitive clicking throughout the cycle? If it is the single click when it comes on, that is the sail switch activating and allowing the gas to flow to the ignitor. There is no problem nor no way that I am aware of to silence the clicking sound. It is part of the design.
We generally camp with 120v power when it is cold enough to require the furnace. Recently, overnights were in the mid 30s. I had the furnace set as a backup to the two electric heaters in case they couldn't keep up. Combined with some upgraded weather stripping I installed, the furnace never came on and the heaters were significantly quieter than the furnace. I ran one heater from the onboard 120v service and the other heater through a heavy gauge extension cord from the power post.
I would highly recommend one or more electric heaters as it also saves on LP usage.
If you do not have 120v service, then you're looking at getting accustomed to the furnace or supplementing in some other fashion as you mentioned. I can't think of any other supplemental heating (not powered by 120v) that doesn't consume O2 or produce carbon dioxide/carbon monoxide (in a worst case scenario) and water vapor inside the living space. The combustion, even a catalytic process, happens inside the PUP with you.