If the cutting tool has top or side openings, those would likely be completely adequate for a small stream of cutting lubricant to pass thru, and insure comple lubrication while cutting (stream fed manually, by gravity or gradually pump fed).
Also, if a small puddle is applied to the interior cutter area before contact with the workpiece, the rotating cutter will essentially pull the lubricant to the cutting teeth as it turns.
Unless you have some high speed cutter application (slinging away the lube) which could benefit from a continuous flow of cutting lubricant, you may just be over-complicating the issue. The normal cutter-pointed-down configuration doesn't usually demand a continuous flow of cutting lube.. cutting into a vertical or overhead surface are applications where I would consider pumping to be a useful requirement.