How embarrassing.
LOL. That's my video.
I was going to build a fan controller at one time and never did. I had heard about the noise that could be produced if you use PWM. At the time I couldn't find a video that demonstrated the noise so I decided to make my own.
In addition to what's been suggested here, you might try a lower PWM frequency. A couple hundred Hertz or less. Supposedly, the noise is less noticeable.
A switching regulator is another idea.
If you go the route of using PWM at a frequency beyond the audible range then you'll likely have to put a fast-decay snubber across the fan's terminals. Otherwise the current will just 'freewheel' and the fan's speed will no longer be a (roughly) linear function of the PWM duty cycle.