If you use a normal wooden preshaped hammer handle and wedge:
Start with a pre shaped handle – they often have instructions attached- the ones I see here do anyway.
File and sand a long gentle taper so you can pound the handle into the head with a lot of force. This requires a good eye or a lot of on and off to try the fit.
While you are at it, sand it smooth to suit yourself.
Drive the handle onto the head with strong hammer blows.
Cut off the extra sticking out of the handle flush.
Drive a wedge in to the wood inside the eye to expand the wood in the eye further.
(For sale right beside the handles)
One trick often used is to drop the hammer head first into a container of oil to soak the handle for a week or so.
It will be taken up by the fibers of the wood which will swell to create a super tight fit.
It will also create a resilient handle which will not crack or vibrate as much in the hand.
Resoak in oil as required in a few years.
In your case, use a vegetable oil which will not contaminate your meat.
Other wise, boiled linseed oil is often used
If you do this oil soak, you will not want to epoxy the handle in as the oil will not let it stick.
Steve