We imperialist's ( .008" dia end mill and .040" total depth ). The end mill will snap in a heat beat ( I'll assume carbide). SO very very slow plunge rate into the material, spindle speed of 20000 to 60000 rpm and cut depth maybe limited to no greated than the diameter of the end mill ....try .005". Clog the end mill and you'll break it. If you have backlash in any axis be prepared to break the end mill quickly. Feed in to fast and you'll bend the end mill and break it. Some spindle runout and you will break it. BTW what's the length of cut on the end mill? $20 to $30 each and it can get expensive quickly.
BTW, for folks reading this ,a human hair is like .003" dia so picture cutting wood or metal with a dirty hair....
Don't know what kind of hardwood as they are all different, grain, knots etc so a little practice on your part for experience will surely help.
For What the above is Worth,
RICH