An effective solvent just requires a few moments of “swishing it around” in the solvent to clean off enough of the existing lube. Shaking or vigorously stirring in mineral spirits for 10 seconds is probably enough, but of course doing it a bit longer isn’t going to hurt.
I personally usually spin on a chopstick to dislodge as much solvent as possible, and then ALSO let it air-dry for a while. If I had an air compressor with a moisture trap, I would use that. But I don’t. 
If you’re going to spin it (or at any stage of the process, really), take precautions suitable to whatever solvent you’re using.