I know this thread is long dead, but for anyone else that ends up here...
If you're a little comfortable taking a few panels off the inside, there is usually a fan that blows cold air from the freezer into the refrigerator section. if you use an external temperature controller, you can extend the wires from the fan and break that connection there, rather than cutting power to the whole unit. This will leave the freezer operating normally, and allow you to adjust the fridge temp with the controller.