Quick update: I finally unpacked the airbrush compressor and gave it a go.
(pencil for scale)
With nothing connected at the end of the hose, the air flow is unusable. But I went back and re-read this thread, and took @BartK advice to use an actual airbrush (and in my case its 0.5mm nozzle), and it gives me a steady jet of air, that while not incredibly powerful should be enough for medium-intensity metal cutting jobs.The good news is that the compressor sustains this steady flow (at around 1.75bar) nicely, it does heat-up a bit over time so as others have mentioned I will probably install a fan over it in my final setup.
I now need to design a piece to attach the airbrush head to the spindle mount, and then proceed with some test cuts.