So what's your budget for this?
Buying an older camper used suggests a tight budget.
All those who commented previously are on the right track.
The easiest answer is to connect an inverter to your battery and use it to run the fridge. When connected to shore power, the battery charging capacity in your WFCO converter will maintain the battery as the fridge consumes it. No fiddle farting around changing power sources or anything. Plug and play.
For a fridge you don't need a pure sine wave inverter, but it would be nice to have and it would treat your fridge a bit better...especially the electronics that monitor temp and tell the fridge when to run.
Such an arrangement will have several sources of inefficiency. Converting 120 volts AC shore power to 12 volts DC to charge the battery, and then converting 12 volts DC to 120 volts AC to run the fridge. Not a big deal in this case, because the most efficiency-"expensive" transformation is a given if running on battery with no shore power.
Budget choice #1
~ Regular Inverter?
~ Pure Sine Wave Inverter?
Moving up in the world, there are inverters that have automatic transfer switch. This is cool, because shore power tells the transfer switch to select shore power and feed that through the inverter directly to the fridge without all the monkey motion through the battery. But if you pull the plug on shore power, bingo, the transfer switch knows and immediately choose the battery as the power source for the inverter. The "big advantage" is that when on shore power the fridge is not sucking on the battery, which, in turn, needs to be recharged at a steady rate commensurate with the fridge's power demands. Automatic transfer switch inverters cost more, and there is a bit more to hooking them up. And if you are really fancy, you can run all your outlets from the inverter.
Budget Choice #2
~ How fancy of an inverter with an automatic transfer switch?
A big expense will be the rather large gauge cable needed to go directly from the battery to the inverter...either way. Large means #6 or #4 AWG wire to minimize resistance with relatively high current running from the battery to the inverter.
No Budget Choice here - Bite the Bullet on some heavy gauge wire.
Others alluded to your real problem...the battery bank. If you have the garden variety group 24 marine 12 volt battery, it can only deliver about 35 USABLE amp hours (AH) before needing to be charged. You'll need a LOT of battery for this arrangement...and a generator to recharge it if you are out for more than a couple days....maybe more than just 24 hours.
Budget Choice #3
~ How much battery and what kind. We're talking real $$ here. Especially if you set your sights son "lithium"...a whole 'nuther conversation.
This is a very big topic. But there are large fifth wheels out there running residential fridges (you know, 20 cubic feet with ice makers) using a similar arrangement. The catch is that they have HUGE battery banks...say 4 golf cart batteries with a combined usable output of 230 AH. You have 35, and they have 230 or more. Get the picture?
You have much to learn and much to do to make that fridge work for you when boondocking. And I didn't even mention $$$$olar yet.