if you have an old AC adapter that outputs somewhere in the 9-12 VDC range, it would be smarter to cut the tip off that and use it instead.

mainly for efficiency reasons... computer PSUs are actually pretty efficient, but not when they are used for such tiny loads like a single small fan.

that being said, there is nothing unsafe about hardwiring the PSU into a constant-on position... there is actually a company that makes a small devices you plug into the cable that would attach to the main motherboard header that shorts the correct pins for you... i can;t recall who makes it though.