Could I use the foot pedal of an electric sewing machine to control the speed of rotary tools?
It would be possible, assuming that the items mentioned all have universal motors and it seems likely that they would. You would need to check the current or power rating of the pedal controller. If it is not marked on the controller, you will need to determine what sewing machines they are for and check the machines. If you exceed the current or power rating, they are likely to overheat and fail pretty quickly.
The controller is probably similar to the subject of How does this circuit control motor speed? That question includes a diagram showing that the motor current flows through an inductor, a triac and an unknown component that might be a thermal fuse. To upgrade the controller, all three of those components would need to be changed. The traic may also need a heatsink.