Six? I count three. One of which is not strictly necessary to get around in in three dimensions. If you can pitch and roll, which are already three dimensional maneuvers in a real sense, you can get along fine. Now, I agree that yaw is a pretty useful function.
Getting out of the shuttlebay already calls for an additional translation - if you can't move straight up and down, you are going to scrape nasty grooves in the floor of the bay every time you attempt takeoff or landing with a craft lacking wheels!
The same with the helicopter-style landings a shuttle is often asked to perform. Under the pull of gravity, you could slide sideways or back/forth by tilting and applying upward thrust, the way a chopper does it, but that won't work if you want to dock in zero gee - you need full three axes of translation in addition to full control over three angles of rotation.
Stick 1 (Ship Direction):
L&R - Roll
F&B - Point Down and Up
Twist - Flat Turns
Stick 2 (Thrust Direction)
L&R - Straffing
F&B - Forward and backward thrust.
Twist (or that additional button mentioned earlier, plus F&B) - Flat up and Down movement.
I'm not sure why you'd need any more?
I'll admit for something more precises (and in less pressured and tense situations) it would be worth using the panels, but if you want to knock your ship out of the way real quick, grab the joy-stick!