Grey squirrels are way tougher than most any other critter. A simple bludgeon of any design is insufficient to reliably kill one, unless hit in the head.
The combination of penetration and shock is required. A washer behind a sharp field point will work. But be prepared for the squirrel to still put up a fight. They are tough.
A bunch of good reading about squirrels can be had at Dean Torges website : http://www.bowyersedge.com/
look under the writings section.