220v AC Fan regulator
Word or warning - TRIAC control will generate noise in the windings of the motor (fan) coils. This can be almost as annoying as a fan running fast. The problem is the TRIAC switching on part way though the cycle gives a current surge and the winding will physically move (not damaging) which makes the deep hum.

Also you need to check that you fan is a true AC fan and not what we call in the industry a EC fan. These are supplied by AC mains but have a internal PSU and then drive a DC fan - TRIAC control will not work on these fans.

However AC fans run very quiet if you run them of a step down transform, auto transformer which is good if you want a fixed speed.

I would suggest looking at getting a replacement fan if you want quiet operation. DC fans are easy to speed control with either a PWM input or by voltage regulating them (DO NOT voltage chop a fan - its kills them). Or look of a fan with speed control inputs, two speed AC or EC fan.

Just worth considering as a option from the start that all.