(2007) International 9400 fridge

It looks like in lieu of a regular outlet there is a cigarette lighter style plug in the hole where my mini fridge will soon reside. I am assuming it is wired to the fridge switch on my dash that way from the factory. My question is how to safely connect said fridge to this power supply. Do I simply use a converter like the one below or is there much more to it? My goal is to not have to run a power cord from the 3000w inverter under my bottom bunk. I'd rather cram a small inverter into the fridge hole and keep those outlets free. Of course the greater goal here is to not burn my new ride to the ground because I wanted to keep my Mt Dew cold...


Thanks in advance.