SynDuo: the 1995 Tie Fighters Collectors CD edition i'm playing, which I thought was only just on dos?
Yes, it's DOS. But when you buy the game from GOG you also get the 1998 re-release which was on Windows 95, as well as the original DOS floppy disk verison from 1994.
Anyway, since you're using the 1995 version which is DOS, the video I linked to should show you how to set up the hat and get it working using the DOSBox keymapper. Is that what you tried already?
If you've tried that and it still doesn't work, then follow StyleWan's advice and check out JoyToKey (or Xpadder) which will let you map your joystick buttons to keyboard keys, so when you use your hat, the computer interprets that as a keypress on the keyboard. I've never tried using JoyToKey with DOSBox but it should work.
EDIT: Only now do I notice that your post title says TIE 95... sorry about that!