Two solutions haven't been mentioned yet: you could use
a nylon-bristle circular brush, driven at such speed that
the drill leading edge won't catch it, at an angle so that
it pushes the chips along the flutes. Even an idler
brush, with a low-friction bearing, would do (the drill
friction will start it up) if you don't mind extra wear.
And in addition to an air blast, you could put some mild abrasive
into that air stream (like coarse sawdust or soap powder).
That adds to the mess, of course, but it WILL scour
without hurting the edge.
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