Hi, two comments.
Finish. Since you can grind HHS, just grind one to the specifications in the classic
Southbend How To Run a Lathe A small tool will work fine.
4 jaw chuck. You may already know, but having two keys is a big help. I'm lucky. My Logan 4 jaw has 1/4" keyholes so I can use two screwdriver handles with 1/4" socket ends. I'm too new with the Unimat to know, but It may be possible to use a handled hex driver with a Robinson bit. Many YouTube tutorials, comes to mind.? I like to read when I can, here is a technique I use from The copy I printed out years ago is now oil paper LOL.
Ron