Is the outlet on an external wall? If so you can drill a hole from the present internal power outlet to the outside of the building. Run a short stub of conduit from the internal outlet to a new water repellent external box. Connect a black to black, white to white, short pieces of wires from internal to external box(s). Being an external box, you must put a GFCI in the external box even though you only have a non-grounded internal box. The will satify the NEC code and provide safety. HTH

Your only problem is when the compressor for the refrigerator kicks on, the lights will probably dim.

and if you trip the breaker, you may not know it until the fridge begins to smell. That's why fridges are required to be on their own circuit.