Changing the fan is a doddle. Avoiding a nasty sting requires you have your wits about you.
disconnect the PC from the mains, let it drain. But, you'll be avoiding the capacitors anyway.
Take note of where the HV and LV sides of the power supply are, the are almost always clearly deliniated. Simple rule, nothing on the LV side will do more than make you go "ooooch", and that's if you are a consumate pillock and shove sweaty paws onto the pins of the caps. Nothing on the HV side of the PSU is any of your business, "THIS WAY BE DRAGONS!!!", mess with anything on that side without being fully qualified and in possession of the PSU's service manual, and you die/fry your PC/set fire to your wife and kids.
Last time I had to change a fan, the connector was a bitch to get to, I could get the old fan off, but no way could I squeeze the new connector in between the caps, and trannies and what have you, obviously I didn't want to mechanically stress any component....so I fitted the new fan, ran it's cable through beside the main multicore, and hooked it up to the Molex loom. I musta stared at it for 20mins running it round and round in my head, convinced I MUST be breaking some fundamental electrical rule. But of course I wasn't, fan was running off the same power, from same place,only the connector had moved. Still, any PSU mod should be checked about 3 dozen times mentally, visually and MOST importantly, mechanically before you even think of hitting that switch.
Remember, ickle wires and ickle components= ickle voltage (and even ickler chance of any appreciable residual charge). Thick wires, big bruisey components and heavy solder tags=big volts=bzzzzzzzzzzt THUMP (potentially even when off, although the caps in PSU's are lightweights up against the HT supply caps in CRTs.....wanna set the olympic long jump record (posthumously by the time you land), shove one of those on your leg.)
Also...no terminal blocks, no tape and no bloody twist+hopes inside the PSU chassis, that way, again, dragons, big scaly bad tempered ones.
If you really are a total numpty, get someone else to do it, one of your mates will have a dad who can field strip a live television without it blinking, ask him to do it.
And if you really wanna do it yourself....take sollace from the fact that 240v PROBABLY wont kill you, or I'd not be here.
Worst thing I ever seen was someone sit on a live benchrigged PSU for a Moog synth, not sure what was funnier, the look on the guys face as 240V when up his tradesman's, or the fact the the Moog did a little Whoop up in pitch when he did it.
Of course YMMV and a teeny jolt could leave you a martyr to MHz
