The ones I have are actually brushless DC motors (BLDC) with a tiny driver board in the hub. Because of this, I'd personally replace the entire fan.
I tend to use cheap computer case fans myself. The three-pin ones are voltage-controlled (nominal 12V; usable range varies from 4V-12.5V to 8.5V-12V depending on fan make and model), and the 4-pin ones use 12V power and 20-30kHz open-collector PWM for speed control but default to full speed when there is no control signal. I've outlined the control scheme
in this post.
One of my own hobby projects is a DIY soldering fume hood from a 60-liter transparent plastic tub with one large side cut out, and an activated carbon filter + hepa filter in what used to be the bottom, and fans mounted on the other side to pull air through the filters, using cheapish known-good PC case fans. Quietness is a big factor, the fume hood -like structure means not that much airflow/pressure is needed. Also the walls allow easy mounting of additional lights. Using two 120x120x25mm 12V PWM PC case fans and
this ATtiny85 based controller I can use a 12V wall wart and adjust their RPM using a potentiometer I can put on a lead (somewhere accessible). Note that these fans have tachometers (two open-collector low pulses per rotation), and that controller varies the PWM duty cycle based on the RPM, and not just based on the potentiometer.
The one cheap USB desktop fan (~100mm, or 4") I ever had (red metal one from Verkkokauppa.com) was horribly loud. It did move much more air than typical PC case fans, but it was so loud I couldn't really use it – but I'm a bit sensitive to high whines (high RPMs), which is why I prefer the larger fans whenever I can. (They move more air, because the area is larger, at much smaller RPMs.)