Many mini fridges have the coolant lines running inside the fridge compartment from the rear wall to the cold plate. You should (actually, must) identify those lines before cutting any holes.
I spent five minutes trying to Google up a parts diagram for a Dynasty 4.5cf fridge. The only hits I got were from others looking for the same thing. No manuals, no web site, no parts references anywhere. You better hope that critter lives forever, because it looks like a disposable fridge at this point.
Anyway, the two things to worry about are the coolant lines and the wires to the thermostat. Either or both could be running inside the liner, or between the liner and the exterior. If you can't figure out what you're looking at, take some pics of the insides and we might be able to help...
Cheers!