Could I replace a stock PSU fan with a more quiet one?

I have done this. It works.

If you're nervous around capacitors, be aware that they can and will store residual mains power. Practice basic safety: Unplug the psu, ground yourself against the case. Snip the wires, strip them, and use a 'decent' wire splicing method. wrapping them with electrical tape is not a good idea. Solder + heat shrink, small wirenuts, "B-connectors", etc.

I've been hit by the caps, you feel it, but it wasn't horrible. As always, proceed at your own risk, but I've done this plenty of times.

I wouldn't recommend fiddling with the rest of the components, but just a simple wiresnip on the fan leads is pretty painless.

Caveat: Some PSU's run their fan on 12V, some on 5V. If you have a multimeter, check and make sure you pick a fan rated for those speeds. Most 5V 'can' run on 12V, but it's not recommended.

No, in my opinion opening the PSU is NOT something you should do.

If you do anything wrong the best case scenario is that you only destroy your computer.

The worst case is that it catches fire and you burn down your house and killing everyone in it.

Sorry to sound alarmist but messing with "out of the socket AC current stuff" is best left to professionals.

It's not problem replace PSU fan, but you loss warranty.

I prefer Noctua Fans