Yup, at least a mouse is required to give fast tracking to the guns up and down as well as laterally. And hit the fire key (left mouse button by default) like a machine gun, taptaptaptaptap...you don't run out of ammo and it'll fire as fast as you can hit the key.
Even then I find it a challenge. A game controller would probably be easiest, but mine is a full control column for flight sims and isn't suitable for arcade style play, so I stick with the mouse and usually get through on the second try if I haven't played it in a while.
Gets my heart beating every time, don't give up on that feeling just for convenience, it's one of the cool features of the game, that and the swoop racing. With a mouse it's not too hard with a little practise and worth it.
To improve this feature what would've been better than the option of bypassing it, would be that if you couldn't down all the Sith Fighters then the Ebon Hawk would load a "ship damaged" module and turn up to the next planet in need of expensive repairs before being allowed to leave the starport.
It is a bit frustrating to have such a finality that you either stay and destroy all the Fighters, or blow up and have to load an earlier savegame. What happened to cut and run?