Place the replacement handle in a wood vise, so that the portion of the handle you will insert into the head is facing up. Tighten the vise.
Coat the outer surface of the hatchet where the small hole is located in the hatchet head with India ink. Touch the side of the hatchet containing the India ink to the top of the new handle in order to mark the dimension of the small hole on the top of the handle. This mark will serve as a guide for trimming the handle to size.
Turn the handle sideways in the vise and remove most of the unneeded wood from the hatchet handle with a spokeshave, repositioning the handle as needed in the vise and using the India ink mark as a guide. Do not attempt to trim the new handle to its exact size with the spokeshave.
Trim the handle to the final size by first removing the rest of the excess wood and giving the handle its final shape with a file. Sand it smooth with a piece of sandpaper. Ensure that the handle fits snugly inside the small end of the hatchet head
Reposition the handle in the vise with the side that goes into the hatchet head up. Cut a slot in the elongated part of the trimmed portion of the handle with a tenon saw. Start cutting at the end of the hatchet handle and continue the cut halfway down the trimmed portion, centered on the elongated part of the handle.
Install the hatchet head on the new handle with the small side down. Drive a hardwood wedge is far down the slot as possible with a mallet to expand the top of the new handle to lock it in place from one direction. Trim the excess off the hardwood wedge with the tenon saw and sand the wedge smooth with the handle.
Drive two steel wedges through the hardwood wedge at a 90-degree angle to the wedge and equidistant from the edges of the top of the hatchet handle and themselves with a hammer. Driving the two steel wedges locks the handle and place from the other direction, completing the replacement of the hatchet handle.