Just my 2 cents worth here:
My trailer is a '63 and the copper gas lines are about in the same condition as they where in some 40 years ago. The 43 year old 110v wiring actually worried me more.
My local RV service center will check out the propane system for 1-2 hours of labor (so about $130) total, which is about the price for a used 110v minifridge.
The nice thing about propane, is that its heavy and stinky.
So in the event of a leak, it will stay near the floor if the leak is inside.
The lines should be run under the trailer, so a leak there will just vent away.
If you do get a leak inside, your nose will wake you pretty fast, aslo there are gas dectors that will go off with a dog fart (yes I have a boxer
The most likey reason to wake up dead when using gas is carbon monoxide, which is the bigger killer in RVs Boats and houses, and scares the hell out of me personally.
I recently "installed" (ie screwed into the wall) a combination fire and carbon monoxide detectore from home depot that ran about $35. Its battery powered and wil allert you before the battery dies, so its seperate from the trailer power.
IMHO you will spend far less by having a pro check out and maintain your gas system than you would in converting everything to electric.