I did cut it to size under running water. Milling the LED recess was finicky enough that, in the end, I dipped it underwater to cool it every twenty seconds or so, to make sure I could still see what I was cutting, rather than having it under water at all times. So, dust got in the air.
I'm pretty sure my lack of experience/poor technique is to blame there. But then again, it's not as if I cut quartz every day, so I think that mitigates the health risks somewhat.