I enjoy making my own things whenever I can.
For turning tool handles I just use whatever wood I have on hand at the time that will work. e.g. Osage Orange, hickory, etc.
I drill the end large enough to accept the shaft. Even a square shaft shoved into a round hole works. I do nothing to secure it since there are no real forces trying to pull it out.
If the tool is for another use I'll grind off the sharp corners of the shaft and grind or file a series of notches around it to accept glue. Then I'll drive it into the handle using a tough glue (epoxy, Gorilla, etc.) to secure.
This all fits in with my adherence to doing things the KISS way. In fact, I have two knives I made when I was about 8 years old using the same principal. The blades are secured into antler handles with hot hide glue. That was about 66 years ago and you still couldn't get those blades out with an act of congress.
"Folks is funny critters."
Think for yourselves and let others enjoy the privilege to do so, too. ~Voltaire