If you feel comfortable getting in there and removing the fan, maybe try replacing the fan with a quieter one? I wouldn't suggest just removing the fan. Lots of heat goes through the psu in many systems.

Yes, as someone with electrical hacking experience:

1) If you're not experienced, or not capable of being careful. DO NOT ATTEMPT. Anyone can learn this, but only if you're willing to be patient and careful.

2) There are two hazards.

2a) One, electrical. Flip the off switch on the back/unplug it, THEN turn the computer on. The computer will briefly try to start on the left over energy in the transformer/capacitors and drain it.

DO NOT use more than one hand on it at a time (other hand goes in your pocket!). It worked for Tesla and it will work for you. One hand means even if you are shocked, it'll go through your hand and out your hand. Not across your heart, killing you. Your hand can take a beating. Your heart will just stop beating. (Pun not intentional...)

2b) DEAR GOD IN HEAVEN. Wear gloves, or make sure you feel for sharp edges. PSU's are made out of stamped steel, which is normally razor sharp at the edges. I learned the hard way, and I ended up gushing out blood from my thumb and getting 6-8 stitches. Do not make any sudden movements like pulling on a stuck wire/connector. It may pop out, sending your hand into the sharp metal. That's exactly what happened to me.

3) Make sure you replace the fan with the same size (duh, but measure if unsure). That includes the depth (thicker might not fit.) And SAME VOLTAGE. Current ratings don't matter much. If it says LOWER, it means it takes less current because it has a higher internal resistance. It won't hurt anything as long as there is enough airflow. Higher current rating will still be okay as long as it's not more than 1.5X-2.0X. These are not sensitive components, there is always working room (if the fan blades were blocked from turning, it might go 5x, 10x or more).

4) If the fan has an RPM wire or temperature sensor, you'll definitely need to get one that replicates it. You'll also need to get the same connector, but if you can solder, you can take the old one off and replace it if you're careful to get the wires correct.

So in closing, there's a lot to it. But if you understand that "lot" it's a simple, and safe procedure.

This does not necessarily make it "safe", either, though it should help. Typically power supplies use active switching to transform the higher voltage (on a buffered line with a giant capacitor or two), so who is to say the switching mechanism stays on long enough to drain the big bad cap near the power inputs? I have a big resistor soldered on two some wire that I use for making sure capacitors are drained by shorting their leads with it. Granted, I wouldn't be too horribly worried unless I was bleeding.

Better than a resister:

light bulb in light fixture with AC cord. Split wire in two, connect the two terminals tp the capacitor terminals. Worst case, keep the lightbulb angled away from your face but the likely hood a cap is going to explode it is almost zero. Light bulb will light up (yes, on DC!) until the power is gone. Confirm with multimeter.

It worked for this one:

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It'll work for any wussy girly man capacitors in your PSU.

Geeze, that looks like a supercap How many F?

Looks good