Firstly, check whether the fan is soldered to the PCB, or simply plugs in. If it's the latter, replacing it is easy. If not, you'll need to splice/solder to get it in there.
As far as safety goes, leaving the PSU unplugged for 24 hours or so should be give it enough time to fully discharge. Try to ensure that when you replace the fan you use one that moves at least as much air as the old one. Otherwise, the PSU may overheat.
Naturally, replacing the PSU fan (or even opening the PSU) will void the warranty.