i have to disassemble a lot of hawks that have that circular wedge arrangement, but without marking up the head;
so i have to be delicate, but i need to be quick, so i can put a new composite handle on and get it out to my investors;
what i do is cut the handle about a quarter to half an inch from the head;
then i get a small drill bit and drill holes around the circular wedge, and inside it, then flip over the head and also drill it honeycomb on the neck side of the head;
then just using a simple screw driver, give the wedge a tap from the bottom side with a hammer or piecve of 2 x 4 - the weakened wood will let the wedge slip right out with little effort;
then i put the head on its side and tap the neck wood a little bit, which is often pressed into the sides of the eye of the hawk or axe - this breaks the mechanical lock and the remaining handle slips right out of the eye.
HTH.
vec