What I did cleaning out my sealed ducts was open the farthest vent away from the furnace -
In my case the duct continued on past the last vent so I blocked this off here with a piece of card board
Then opened a duct vent on the other end of the trailer and used my leaf blower and blowed thru the duct work. All kinds of trash then came out of the other opened end... Didn't have a dead mouse but it should have blown him out of the duct doing this.
Some folks have good luck using a small mirror that will fit down in the duct vent and by shinning a flashlight on the mirror you can see down the ducts...
Most trailers are sealed up on the bottom and that would be a major undertaking to remove the bottom membrane to inspect the duct work.
On brand new trailers the furnace itself will put off some bad smells when first used until it burns off all of the new prep stuff. I even don't like the normal smell of the propane being burned myself... That bothers us as well...
Give the leaf blower a try...
Don't be too bad on the little critter fellar - they got to survive in this world as well...
Roy Ken