Veritas® flush-cutting saws have teeth that are set only on one side of a thin flexible blade. This allows them to trim protruding plugs and dowels without damaging the surface. They cut on the pull stroke.
The single-edge saw is $20, and the double-edge version is $25. Both saws are about 11-1/2″ long with 4-3/4″ blades and 22 tpi.
Lee Valley [Manufacturer’s Site]