Hey Jim,
if you really want to collect dust from the usual machines in a carpenter/cabinetmaker/wood workshop with a professional dust collection system, usually you have an automatic dust collection startup, e.g. like this one which uses electromagnetic sensors over the power cables to sense if there is current to the motor of a machine, (would work with spindle cable too), and which also switches the sliding gates.
But to your question with the switches/relays:
First I would not switch the dust collection and the spindle coolant pump by the same output, because in some situations the coolant on the spindle needs to run when the dust collection does not. E.g. the spindle coolant would continue to cool after the spindle was stopped as long as the spindle is still hot or warm, or, when you mill non-ferrous metals, the dust collection is useless and you would not want it to run (while spindle coolant pump of course has to run) but instead switch on workpiece air cooling or workpiece fluid coolant/lubricant nozzle with M7 or M8 (this creates another problem that is solved here).
As far as I know the VFD PwnCNC sells has only multi-purpose relay outputs but no open-collector outputs, so I am not sure if your IoT relay (FAQ) will work on those VFD outputs. Relay outputs on VFDs are usually SSRs which are not really relays but semiconductors (thyristors or triacs) which need a minimum load current to flow to reliably hold their state, but the IoT relay advertises that its control input draws only absolutely minimal current. I say “usually the relay outputs on VFDs are SSRs”, but you can ask Daniel @PwnCNC if this is really the case on his PwnCNC VFD, or ask him if he connects a relay on these programmable multi-purpose relay outputs or other loads. With their max. 3 A current @250 V, these outputs cannot drive a shop vac or a dust collector directly as that would be 660 W maximum at 220 V (they could drive a coolant pump though).
Usually on a VFD, you use the open collector outputs to control the spindle coolant and dust collection relays. But as far as I can see the DELIXI CMD-EM60 has none (am I right?) And I would use real relays, e.g. Omron G4A (can switch 20 A).
The VFDs Omron MX2 and Hitachi WJ200 (which are practically identical), but also many other VFDs, have two open collector outputs (here called “11” and “12”):
Regarding the wiring of two switches that switch an electric device like dust collection on, what you describe with a SPDT (1 x UM, Wechsler) switch requires that you manually have to decide who gets the dust collection. Also you switch only one conductor (switching both is better). But you could also put the switches in parallel. A relay is also considered as a switch here, e.g. with two DPSTs (2 x EIN, Schließer), of which one is a relay:
