I did this about 8 years/30 cord ago. The wedge under the one lag is one of the circular tapered steel wedges. Drilled 1/4" holes and ran 3/8 lags in. Hasn't come loose yet.
I broke my fiberglass handle from Lowes, went down to the local hardware store picked up one that was a "close fit" and hung it on the handle. Jammed the wood chip in, hammered the metal wedges in and it held on for about 2 years. It is now time to replace the handle as a few hard pieces of oak with some knots gave in, but not without a fight.