Some years ago I discovered some Stanley chisels in an old box - the ones with a black plastic handle - that had survived since the '60s, albeit with murderous damage to the plastic, (mainly burn marks from welding that was too close).
They were really kerbergered in the handle department.
I decided to re-grind the cutting tips and sharpen then up for use as secondary hacking-chisels. That was, if I could rehandle them in the process..... otherwise they'd remain paint-pot-openers.
The old plastic handles came off without too much resistance. This meant that they were not 'hot-moulded' on, as some newer plastic chisels might be.
The shank was secured in a vice, pointing up. With the assistance of other old chisels, a set of large mole grip and a degree of hammer-persuasion they came off clean. . The tangs were circular in cross section, about 2 inches long, with a pronounced bite shape out of each side to prevent rotation.
The next step was to turn some new handles. I retained the same size and shape and recreated it in some old Apple-wood that I had in the odd-and-sods box.
The tang was, if I recall, exactly 3/8 inch diameter, most inpotartly it was an exact size of a drill that I had. The side bits were about 1/8 inch wide and I could cut a slot on the insides with a narrow chisel and I'm glad to say that it was a good, clean and very tight fit.
Somewhere I may have some photos of the whole thing, because I wrote it up, with pictures...... I'm off to have a look.
In short, It can be done....... for some chisels, if it's worth it.