Squaring a drilled hole. Begin by drilling through the leg and tenon with a bit just smaller than the width of the peg. Make sure you don’t drill through the other side of the leg. Use a 1/8″ chisel to square up the first third of the hole.
Making peg stock. [Irrelevant – SW]
Whittling pegs.With the pegs cut into 2″ lengths, round over the first third with a small knife. Rounding the ends of the pegs prevents then from splitting the legs.
Driving it home. After applying a small amount of glue to both the peg and the hole, tap the peg with a hammer. Keep the peg aligned and stop hammering when the peg bottoms out (you’ll hear a change in tone); otherwise, you risk splitting the leg.
— p.65, Fine Woodworking, Taunton Press, Jan/Feb 2001.
So perhaps I do not need to make a pencil sharpener after all! I have been trying to make round treenails, using some varient on the idea of a plane I saw in use on Duyfken; I’ll give this simpler idea a go.