I wouldn't be scared of 120V, but you do have to take the usual precautions. I'm not sure a dimmer switch is the way to go. I don't think they work on electric motors the way they work on lights. Might be you just need the correct type of electric motor.
That said, 12V fans are a dime a dozen and lots less of a bother to play with. You can control the speed with a very simple, or very cheap, circuit you can build or buy. Or just run a lower voltage, say like 6V-9V. I've used a volume pot to control my original stirplate and I built a PWM circuit to control a newer model and both worked fine. The PWM curcuit allows for more speed range and finer control, but a decently built stirplate shouldn't need all that control.