The amount of coolant inside a fridge is actually pretty small, it's only a few grams. You would have to install an extraction chamber which could be opened, valves to isolate it from the butane-filled part, and some means to get the oil out (oops, you said all that yourself). You also have to make sure that your extraction chamber will not contain any air before you let it run. Finally, the fridge pump contains an oil, and you have to somehow make sure it won't contaminate your product!
Sounds pretty involved to me, you could only extract a small quantity anyway amd the butane would constantly have to be replenished.
I'd rather distill the butane off and condense it with CO2/acetone. You might even build some semi-continuous apparatus, but I doubt it's worth the trouble. I'd rather try to find a good and cheap butane source.
Or experiment with other solvents, e.g. first extracting all the goodies with hexane, and then extract this stuff with butane (after being applied to an absorbent like SiO2, cellulose etc). Well, you could also investigate chromatography, which allows you to reuse the hydrocarbon solvent.
I'm not fat just horizontally disproportionate.