I think you can tie the two black wires together (ground), and then splice the yellow, black, and red wires into the corresponding wires on a three-pin connector. Red is power, black is ground, and then the yellow wire is the RPM feedback, usually negatively pulled-up (that is, a circuit sends positive voltage through the yellow wire to ground, and when it measures a current, it knows it's gone through a revolution). You can cannibalize a three-pin extension cable -- that's what I did in my own machine. the extra PCB from the PSU isn't necessary-- it's just an automatic thermal speed control circuit, most likely.
Disclaimer: I don't guarantee that you won't smoke anything by following my suggestions. But that's the risk you take whenever you try to mod something to fill a different purpose than that for which it was originally intended.