It's a Brown & Sharpe cutter all right, and has been bounced around so much the cutting edges are basically worn smooth.
I wonder if the 1921 date is accurate.
As for no keyway, that looks a lot like the cutter used in a keymaker- that is, the little machine used to duplicate door keys and the like. Not much cutting force on those, 8usually in brass, and the fine tooth count makes for smoother cutting.
Doc.