It's supposedly better to short capacitors with resistors to discharge them, but I still think it would be risky (to the health of the PSU) while they're attached to a circuit board.
I would suggest doing the cut-n-splice method that prophase_j mentioned, while being careful not to come in contact with other components of the PSU. Not as pretty, but it's less invasive (you don't have to access the circuit board of the PSU, and you may save yourself some disassembly).
Most fans are in the 5-12 volt range and vary their speed by the input voltage, but some have a 3rd wire (usually yellow I think) that reports speed back to the host device so that it can shut down if the fan burns out.
Also, make sure the replacement fan moves the air in the same direction, as PSU fans are meant to be the main source of airflow in most computer cases. Usually PSU fans exhaust hot air out of the PSU, which causes cool air to be pulled in from the front bottom of the computer case and across all of the components before it reaches the PSU.
I've worked with electronics quite a bit, but I haven't opened many PSUs. The coolest thing I've done with a PSU is jumper some pins in the motherboard connector of an ATX PSU to make it turn on whenever it's plugged in, so that my roommate and I could use it to test a window+LED mod he was making to a 5.25" DVD drive without having to keep installing it into and removing it from his computer.
As for CRTs/TVs, they're usually relatively safe to handle unless you mess with the plunger on the tube. I've opened up a lot of old CRTs to adjust the horizontal output transformer in order to correct for them going dim over time (beyond what could be adjusted for via the front brightness knobs). If I had the guts, I'd play with the convergence rings on the yoke, but I'd rather just buy LCDs to replace most of them instead 😀