Given a choice I would likely start with
something like this. They are self powered and passing a few turns of your hot mains power going to your power tools would have them come on at a pretty low power tool draw. The units driving an Amber LED likely have a few volts out to the LED when the min current flows through the mains power. Those units happen to be CR Magnetica but I am sure there are other distributors out there of the same or similar current sensors. They cost a few USD as I recall. So pretty cheap starter.
Maybe use the LED out to just drive an SSR module (solid state relay) for your dust collector and just place a switch across the SCR so you have manual or auto operation.
A SSR similar to
something like these would work for you. Depending on how much current the dust collector draws. A zero crossover 10 Amp with a 3 to 32 volt control voltage should work for you.
<EDIT> You may also want to give
this thread a read. It was started later today. </EDIT>
Ron