My thought is to feed the project with a vortex cold air gun. It
attaches to compressed air and supplies air as cold as zero degrees
Fahrenheit.

One company I worked for bought one for some lathework that had to be
kept cool, but could not take coolant.

If you should decide to go this route, use dry air for the feed.
Otherwise, moisture will condense and freeze in the discharge nozzle
and cause the gun to shoot tiny ice balls around the room.