For something Like a hawk handle, where it going to get a lot of handling and use, Use the tung oil to seal the wood, 2-3 hand rubbed coats. Then finish with a couple of coats of Tru-oil, which has driers and will leave a nice gloss, or matte finish, depending on what you want and how you work it.
For a matte finish with Tru-oil, you can either wait until the finish dries, and rub the finish lightly with pumice powder, or Rottenstone( buy from a paint store) Or, 10 minutes after the Tru-oil sets up, drag your damp finger lightly across the finish to break up the glossy reflection. The dried finish will be matte, after doing this. Try this technique on a scrap piece of wood, to get the hang of it, but once you see how easy it is, you won't be buying rottenstone or pumice powders. You will know that the finish has set up because it will get that wet, waterglass look, without streaks.