Yeah, have a care what fan you choose for replacement. Many power supplies, especially 'quiet' ones, run their fans at very low voltages when idling, and not all fans play nicely at those speeds. PSU's with 120mm fans (such as Corsair's HX series) will give you the largest number of replacement options.
PSU fans typically use two-pin connectors, so you'll have to adapt your replacement fan's three/four pin connector appropriately. Any re-wiring/soldering that you do, make absolutely sure you
fully heatshrink/insulate the result so that you don't short anything out when you cram everything back into the unit. And make sure you point the fan the right way! (Gosh, no, never done THAT before

)