I have tried ever possible way in the world to drill by hand with consistency. Given you have a sharp and straight bit. It still tries to wonder around because of the chips and the heat. I have lucked up on a few, but ruined alot of nice hawk handles. The best way, if you are set upon doing it yourself is the laminated way like has been mentioned. Or buy from Dunlap.
I do drill my own. But I do it on the lathe with handle in the chuck and turning , and the drill bit in the tail stock. I use a 1/4 gun drill which has a hole down the middle that I blow air thru. There is a groove down one side to evacuate the chips and I still have to go slow.