Seconding what Belegedhel said, a 2-way RV fridge is only going to make a tiny bit of noise when igniting the gas burner, and some installations require a fan to move air across the heat exchanger in hot weather.
If you are remodeling a trailer and need some huge amount of cold storage, I've seen setups with 2 gas-electric refrigerators, but the suckers are expensive so that's a tough sell.
While it would not be silent, if you wanted a bench with a top-loading fridge built into it you could build a cold box and buy a Danfoss compressor with an evaporator and condenser as a kit. Well-insulated setups like that are very efficient since they don't lose as much of the cold air inside when you open the door, but I think you'd end up with a full-custom job and again it wouldn't be silent when the compressor is running, though they're pretty quiet.
Il Carriaggio — 1975 Argosy 24 | Il Progetto — 1976 Argosy 28 Center Bath | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill