Not sure why you want to by-pass the thermostat and build in the STC? Making a separate STC project box and just plugging the frig into the box is not only the simplest method but also make the STC portable/reusable on other set-ups. AND allow you to convert the frig back to a frig. Which is why I went in that direction. Now if my frig craps out or I decide to change things around, I just unplug the frig and plug in the next appliance.
But, if you're bent on integrating it...
Looking at your Danby wiring diagram, the black wire going into your thermostat is the Line/Hot wire from the plug on your frig. That black wire will be the new feed for your STC. Disconnect it from the thermostat and connect it to the Term #1 & #7 per the STC diagram below.
Note: It is difficult to see the terminals and which wire physically connects to the thermostat. You'll need to identify this wire yourself.
Then, disconnect the red wire coming out of your thermostat. That red wire will connect to term #8 (blue wire) in the STC diagram below.
Next, connect the white/neutral wire coming from your frig plug to the term #2 per the STC diagram below.
Last, the big white wire coming off the back of the thermostat is the temperature prob. It is no longer needed and can be disconnected.
But if you clip it off, there won't be any turning back...
The yellow/green wire is ground. The chassis of the frig should be grounded where the plug cable comes into the frig so there should be nothing needed for grounding now that the thermostat is removed from the circuit.
Disclaimer:
I'm an engineer but NOT an electrical engineer. Wire at your own risk...
Good luck!