Our 3-burner LPG stove with oven, never emits the smell one typically detects when opening the valve of an untapped cylinder. As was mentioned, a very slight odor may exist for a second or two before igniting the burner - but VERY slight. During use, no smell should exist.
Similarly with our LPG, on demand hot water heater - no odors. In addition to typical solenoid switches at the valves in exterior tank lockers, ABYC codes require all appliances (and separate burners) to have integrated safety shutoff devices on gas lines, engineered to cut off gas flow if no flame exists. Electronic ignitors are also required - no open pilot flames are allowed.
It may be possible that one of your burner's safety valves is defective, therefore it emits gas when another is in use.
A propane sniffer is also a smart accessory - which should send an alarm if propane is detected in the bilge areas - where a leak would allow it to migrate to - being heavier than air.
I would suspect you have a leak at an appliance, fitting or tubing line.
True Blue . . .
sold the Nauticat