Knock the old handle out, then epoxy the new handle in place
Photo 1: Drill out the handle
Cut off the old handle just above the tool head. Open the jaws of a vise wider than the remaining wooden handle plug and rest the ends of the tool head on the vise jaws. Drill 1/4-in. holes in the wooden handle plug until it looks like Swiss cheese (drill around the metal wedge in the center of the plug).
Photo 2: Persuade the wooden plug
Knock out the wooden handle plug from the top of the tool head with a hammer and the biggest bolt you can find in your shop or garage. It takes a couple of good whacks with a hammer to get the plug started (so take a big swing), but once you get it going it'll push right out.
Photo 3: Insert the handle
Clean the inside of the eyehole with sandpaper or a copper fitting brush. The scuffed surface helps the epoxy bond. Insert the handle core into the tool eyehole until the top is flush (Photo 4). Seal the gap between the handle and head with the supplied caulking cord sealer to keep the epoxy from leaking out.
When you're swinging a big-impact tool like an ax, maul or sledgehammer, every miss takes its toll on the handle. Eventually the handle will break or the tool head will loosen. Replacement wooden handles secured with wedges are OK, but for a few dollars more you can buy a replacement fiberglass handle that could still be swinging in 100 years. The kit contains a fiberglass handle and an epoxy packet. The epoxy and hardener are in one packet with a divider rod in the middle. When you remove the divider rod, you can mix the contents without mess or smell.
Photos 1 and 2 show how to remove the most stubborn old handle. Next, clean the inside of the eyehole (Photo 3). Epoxy won't bond to rusty or greasy surfaces. Insert the new handle and bounce the bottom of the handle on concrete if you have trouble getting the top of the handle core flush with the top of the tool head. If they're still not flush, file or carve the new handle to fit.
The epoxy mix (Photo 4) will seal all the gaps between the handle core and the sledgehammer head, but it must be thoroughly blended or it won't set up. The temperature needs to be between 75 and 115 degrees F for proper curing. Pour the epoxy between the handle core and the hammerhead as shown in Photo 4. Wipe off any excess and let it cure for a week before using the tool.