I'm not sure if this idea will work, just throwing it out there for comments:
Could you possibly use an industrial "delay on off" relay?? and install a small separate DC supply (not another computer supply) which is wired to the AC input to the computer "before the off switch" so it is always on. The main (computer) power supply would be the input to the time delay relay's "coil" and the fan would be powered through the additional supply through the relay's "contacts".
When you turned the power off on your computer the relay would time out after a set amount of time as determined by the relay. But, as long as the relay remains on it would supply power to the fan via the "always on" DC supply.
This relay shown in the link below is way over-kill, just showing some of these are out there; only did a one minute search on the web for delay on off relays.
The small DC supply would draw very little current so it wouldn't be a waste of AC since it is always on. It may be a good idea to have a seperate fuse for it though. Also you would have to match up the DC supply specs for the fan (voltage??). Also, because you are powering the fan from the additional supply it won't be monitored (nor powered) from the motherboard (good/bad idea???).
Another way may be to add a large capacitor across the fan and have the capacitor power the fan after shut-down. A little more research will be needed as I don't know the load that the motherboard/power supply is capable of in charging the capacitor (thru a series resistor).
Anyway it seems like a lot of work for this problem (that may not be a problem after all).
Any suggestions?? Good/Bad idea??? Remember, just throwing this idea out there for some others to "think out loud" about this idea (as I have done).
Relay Link