What could cause a desktop power supply to "hiss"?

Working many years in IT repairs I came across plenty of power supplies that did this - and only once in my whole life did one actually blow up and scare the living poo out of me!

The hissing noise is damaged voltage regulator- caused by failing components like you mentioned leaking cap ( does not actually mean its leaking- its just not charging to spec any more; hence-leakage- Such damage can also be caused by voltage spikes/dips or my favourite- lighting!) This over time causes damage to other components which causes a general failure.

The hissing noise is a bad sign and means that the power is not stable and could be potentially dangerous to the rest of your PC.

I suggest replacing it straight away. as trying to fix the problem would need extensive knowledge in electronics especially in AC/DC Conversion and understanding how each channel is split. normalised, regulated, blah blah blah..

And yes opening a power supply that has been recently plugged in can give you a shock- not lethal- but not pleasant either. You always need to discharge the large caps to the leakage part of the circuit.. which can be anywhere/ or grounded ground(meaning connected to your ground in your house!)

A few Dollar and your safe again.