I used 5/16 sq x 6" long steel.
I used all sorts of wooden styles for 10 years or so before those and found the solid feel and heft of the steel made for alot better cutting.
Brass would be fine too I'd imagine. Aluminum too light for me but everyone is different.
I bought a dozen of the handles commercially made from N-Graver in CT. at the time and never needed any more of them.
They sell them as a Belgian style graver handle.
But it's certainly something you could make yourself.
They have a set screw on the side to hold the bit in place.
I used to drop a small steel plug down into the hole to boost a shortened bit out a little to take advantage of some more of it's usefull length. When they get down to about 5/8" long, they're about spent.
I've got alot of those around, mostly carbide. They still come in handy on other projects once in a while.
They worked well for me for 30 years or so.,,and yes even they will peen over on the end from the hammer taps if you work with them long enough..
They've been retired for the most part now though. For the last 4 years or so it's been an air assist graver to do the work. Not my choice, I'd have stuck with the traditional tools given that.
But age, accidents and nerve damage makes choices for you. It allows me to still do what I love to do.
http://www.ngraver.com/ I think they are $7 each now. Click on 'price list' for the current $$.
Or make a couple for yourself.
Just before my left hand really gave it up, I wrapped some of the handles w/ thin stretchy leather to cushion them more and make for a better grip. Something I never needed previously.
That would work nicely with any handle material chosen especially for those 8hr sessions at the block.
If I made one, I wouldn't bother with a depth adj set screw for the bit. Just a blind hole w/ a set screw from the side to hold the bit in place. Use a booster plug when the bit gets short from sharpening if you like. But I think a set screw in there would most likely get rivited into place quickly from use. Even a booster plug should be hard and undersize to avoid that happening.
You won't notice the very gradual shortening of the bit during use from sharpening. There will be a point that it will start to feel too short while cutting,, and that is the time to replace it.
There's alot of sharpening stone time done to get there though.