You can accomplish what you’re wanting with a battery master disconnect switch, and avoid creating a new failure point for your fridge. If your trailer doesn’t already have a master disconnect switch that completely disconnects the house batteries, I would install one anyway.
The switch and the wires would need to be rated in excess of the full load from the batteries.
This is how my master disconnect switch and fridge work:
If the fridge is set to run in DC, LP or AUTO, when I set the master disconnect switch to OFF, the fridge turns off. When the master switch is set to ON, the fridge turns back on in the same mode it was in before.
This assumes that the 12 VDC circuit from the tow vehicle is either switched off when the ignition is off, and/or is switched off by the master disconnect switch.
You should of course make sure yours works the same way.
:):)