When Tom, a friend, taught me how to fit hammer handles to heads for my mechanic broken off handles, we used a shaving horse to hold the handles and spoke shaves to fit them. And we used two inside caliper gages to set one for the large distance and one for the short distance. We transfered these to two dimensions, to outside caliper gages so we could test our handles to make them the correct shape before testing them into the head.
Once they were the correct size we placed the handle into the head, and seated it to the correct spot. Then we drove in a prepared hardwood wedge to flair out the handle end, cutting off the excess wedge once it seated to the bottom of the kerf cut into the handle.
After the hardwood wedge was seated, we then drove in a small metal wedge on and angle to the hardwood wedge and this secured the hardwood wedge, as well as somewhat flaring the handle out in the other direction.

If it wasn't mentioned to you, ever, don't soak a handle in water to expand it into the head, this will only damage the handle and cause it to break off later on.

If you're not using dry wood, one method to attach a handle is to place the end of the handle, that is going into the head, into a pail of sand, which is on top of a heat source like a stove. This heated sand will dry out the handle end a little, making it easier to fit into the head.

Once secured into the head, the moisture in the handle will equalize back down into the head end and swell it up a little and hold it tight to the head, letting it all dry out evenly together.

Good luck.

Jim Rogers