Real tung oil will always result in a glossy finish. There are some products like Formby's that aren't really tung oil, but come in both glossy and more satin like finishes. Do you intend to fill the grain? You can apply tung oil without filling the grain, but the grain pores will still be real noticible; but that shouldn't be an issue if you don'y want a high gloss, mirror like finish like you might see on a number of axes on this site.
Since it doesn't sound like you want a "mirror" like finish, don't sand/grain fill it to start, you can probably get away with 4-5 coats of tung oil, wipe off all excess after applying each coat and buff back with 0000 steel wool bretween coats.
If you want no gloss/shine at all, it might be easier to just use 3 coats or so of clear "wipe-on" Minwax stain poly.