You're over-thinking it, worrying about the angle.
Bore your hole first, file the shaft with a mill file so that it goes in tight by hand (with the handle in a vice and some hard twisting) and file about a sixteenth of an inch from the front and back of the hole, tapering all the way down through the head.
Then split the handle crossways with a narrow bladed saw, insert handle, insert wedge, & tap it in solid. Oil it up a couple of times and everything will swell even tighter.