Quick simple wiring question

I just bought my AC unit for my reach in cooler. I also ordered a thermostat with a piggyback plug.

Question is this: as near as I can figure all I have to do to rewire my AC to work with this unit is bypass the internal AC thermostat. There are two wires connected to the t-stat. If I just direct connect these two wires I am good to go, yes?

I am starting the actual construction of this unit tomorrow. Kind of excited. The final footprint that I have decided on is 3'5" D X 5' H X 6' 5"W. It will have two reclaimed refrigerator doors on the front. 30" W X 48" H each. The total fridge space will be 90 cubic ft. Enough room for up to a dozen kegs, plus 6-8 cases of beer and another couple cases of white or sparkling wine or cider. Plus room for two full carboys.

I also plan to build a 2' extension that will serve as a manually vented fermentation chamber.

I will be chilling it with a 6500 BTU AC and a no name prewired t-stat .

Don't listen to me but yeah that's what I've read a number of times now...

The best thing to do would be to take a multimeter (if you have access to one) and measure the AC voltage across those 2 wires to make sure they're the correct ones.