Easiest way to fit a square peg in a round tool handle .... make a square hole!
Set up table saw with a dado stack 1/64th larger than your steel bar ... cut half the depth in one half of your handle blank, and half in the other half ... stop the cut before going all the way through the handle blanks ... you want what is called a "blind dado". Glue them together to form a square hole. Use wax paper over a scrap section of steel bar to prevent it from sticking to your wood glue in order to give proper registry for the square hole - make sure the end of the steel bar scrap stock sticking out has been center drilled!
Once the glue has set up, (DO NOT use gorilla glue ... the wax paper will never come out!) turn it round on your lathe (use center hole in the scrap of steel bar to keep things steady in the tailstock end, chuck the other end up in your chuck jaws ... when ready, just part it off and finish sanding/finishing by hand). Turn your desired handle profile, the tenon for your ferrule, sand, seal, and finish ... then go back and part the back of the handle off. Use caution when determining you length while parting it off, you don't want to cut into your tool's tang hole!
Knock the scrap steel bar out of your tool handle and securely epoxy the real tool in place ... don't forget to take a cutting wheel to the tang that will be in the handle, to give some nice sized notches for the epoxy to really grab on to (perhaps 1/4 inch deep here and there down the tang length). Use a 24 hour setting epoxy for best strength, I think ...
Now, keep in mind ... I invented the "ventilated carbide tipped tool handle". Please don't copy my terrible mistake!