You can always just torch it at that specific area to char the wood pieces enough to loosen and soak it in water. ... it won't affect the temper of the edges... you'll have to get it really hot to affect the temper.
No need for any heat, like the others have said use a chisel and punch and knock out the old wood, i do it all the time very easy not rocket science. Buy a new handle and you will be back in business in no time.
That's an awesome find! You might not even need to drill it. If you can get a screw into the wedge and pull that out you may just be able to hammer it out, easy.
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Drill it and press it out. Perfect use for those old dull drill bits you haven't thrown away yet. The heels don't look worn on one side so it looks like it didn't see much use before disappearing. But the blade bevel profiles are just not right, they are way too convex. You should re-grind and sharpen both with one bevel 'fatter' than the other for dirty work around roots/etc and the other 'skinnier' for chopping and limbing. Use gloves when you sharpen it.
The only mark is a M on one side.
I found a large single blade axe head but it has a crack right down the middle. It would fly off a new handle.
I found a smaller 3 tine pitchfork head. I'm going to restore that for use also.