Just be careful when you're working inside the power supply...the big capacitors hold a charge even when unplugged. Just open the PSU case and cut the power wires from the fan close to the PCB so you have some wire to work with.
What kind of power connection were you going to use? A 4 pin molex or a 3 pin? If you're using a 4 pin molex the easiest thing to do would be to get a 3 pin to 4 pin power adapter and use that...cut off the 3 pin connector and splice the wires from the fan to the 2 wires from the power adapter. I solder the spliced joint but you can use butt connectors for that. I cover the joint with heat shrink tubing.
If you're going to use a 3 pin connector to connect to a motherboard fan header you're going to have to find a 3 pin female plug. I usually get mine from old fans but they do make 3 pin to 3 pin power cord extensions. Or you could get lucky and the PSU fan will already use a 3 pin connector.
Cricket