Bottom Finish in Tiny Pocket

Hey Y'all,

Just started machining metal after making cabs for a few years. We have a photo stencil in the shop. A mandrel for making micro processor chips. It's made of stainless steel with a super high mirror polish on it. right now we are making a .002" deep pocket with a .005" RAD, .040" DIA cutter. We then use abrasive wax to polish the bottom of the pocket back, but this makes the high mirror finish that is on the work piece foggy and requires several steps to clean up that risk more abrasion. OK, so the question is: Is there a way to get super high finish in the bottom of this pocket without touching it? A cutter or tool that will do this without another human step?