Current sensing relay that momentarily closes contact each time state changes
Follow the rules
The trick with anything that that which uses AC mains, is complying with Electrical Code rules for handling power.  To name a few:

Equipment must be Approved, generally by UL (and that means UL Listed not RU-Recognized)... and you must use it according to labeling and instructions.
AC mains wires have to be entirely inside AC mains wiring methods and enclosures (e.g. Class 1), and low voltage circuits cannot be in the same cables or enclosures unless the entire low voltage system is, soup to nuts.  No ins/outs, unless optical or wireless.

The problem with hacking the wireless relay is you're working way too hard to save a relay, which is a readily available commodity, and it also makes control more complicated than it needs to be.
You could have a circuit entirely inside the box with two Current Transformers -- one clamping a dust collector wire and the other clamping a bundle of wires (1 hot from each tool; CT doesn't care how many wires are in it). It would look for &quot;disagree&quot; (tools on CT off, or tools off CT on) and send the signal at that time. But you'd need to hack the pushbutton to achieve that wirelessly, unless you wanted to do something optical to get out of the panel to your chosen relay. See what I mean about 'too much work'?
The simpler way: Dust collector on when load is on
And for that, we can use an approved enclosure -- the bog-standard AC mains circuit breaker &quot;sub panel&quot; that is surely already in the wood shop (or you will really benefit from having one).
And we can use approved switching equipment - either... a) A Honeywell Aube (which supplies both a large relay and a 24 volt AC transformer to power the relay; it has 2 terminals, shunt them to make the relay pick up).  Some Aube's bring out a third terminal, giving  you both legs of 24VAC so you can power other small stuff.    Or, b) do it with separates: using a UL-listed general-purpose contactor (not a specified-purpose contactor for A/C, etc.) and a COTS $13 24V thermostat transformer.   All this lives entirely inside the subpanel enclosure.
The relay is wired to interrupt (a) hot wire to the dust collector.
So now, all we need is a current sensor that shunts (shorts) 2 wires when current is flowing.
Sensing AC current
How do we sense circuit current being active?  AC electric wires throw a rather considerable Electro-magnetic field or EMF.  So do DC wires, but theirs is static, like a refrigerator magnet; AC is like a refrigerator magnet that is spinning.   If the 2 circuit wires are together, the EMFs cancel each other out.  But separated, the EMF throw is considerable (everything between them becomes the core of a transformer). And that's part of why AC wiring rules are so complicated and counterintuitive.
Magnetic reed switch - closes on as little as 10 ampere-&quot;turns&quot;.  (a wire passing straight by it is a &quot;turn&quot; thanks to the magic of AC EMF, i.e. the thing that makes transformers work).
You can wrap the wire multiple times to increase effect by that many times. Passing the return wire (e.g. neutral) by in the opposite direction also counts as 1 turn.
At that point you're just running the normal, insulated wires past the reed switch.  Noting the two wires powering the tool throw equal and opposite EMF; if they run together the EMFs will cancel each other out. So, use that to your advantage in placing the reed switch.
You do all this inside the subpanel, so you have a nice Code legal enclosure for all this stuff.  You're not even piercing any of the circuit wires, there's simply no need thanks to the magic of AC EMF.
The low voltage 24V wiring is entirely contained inside the subpanel, and since it's all contained within Class 1 wiring methods, it doesn't matter if it intermixes with AC mains voltage.
How is the magnetic reed switch going to pass inspection?  Granted, you're kind of throwing yourself at the mercy of the inspector... but since it's entirely inside an enclosure, 24 volts, insulated with shrink tubing (right?) and nothing is happening except normal, insulated wires are being routed near it... there's not much to fuss about.