You need a load sensitive switch - basically a current driven relay rather than voltage. You arrange for loads that need dust extraction to run through the switch, switch detects the load current & operates the DOL starter. The starter needs to be wired for external control rather than latching on the push buttons (or get one without buttons), and as suggested it would be a good idea to have a run-on timer.
Rather than buy a cased starter, might be better to get a DIN rail enclosure and mount the contactor, timer relay, and current relay in the one box. I'd be inclined to put the case on a board with a mains cord (or power inlet) and 2 separate sockets - one for the extractor unit, the other for the load.
As an idea of what's available, see
this selection at RS
You need to look at minimum current sense, maximum current capacity, supply voltage, and switching type/capacity. Some put the sensed current through the device, others have a CT (current transformer) sticking out the front that you feed the load supply (only one) wire through.
EDIT: TBH, I suspect that by the time you've priced it all up, you'll decide it's not worth the expense to avoid having to flick a switch