Another way would be to run the motor on Dc, this could come from a smps operating above audible frequencies, however motors run on Dc are more difficult to control than Pwm as the torque is less due to the dynamo effect in the motor, you can reduce this effect by using back emf as part of a feedback loop in the control system.
This gets complicated and if you dont have a scope then its probably not something you'd want to try.
To find the switching speed of your existing motor, download some software that will generate tones at a fequency you want using the sound card, fire up the motor and adjust the tone so that it matches that of the motor, you'll hear a 'beat' as the tone freq approaches that of the motor which will stop when the 2 are matched, the frequency of your tone will then be the switching speed.
My battery power drills are about 4 khz.