What about holding the Joystick in his right hand and throttle in the left makes the Avatar "Right handed"?
I'm left handed myself but use my controllers the same way set out in the game. Changing the Avatar to being left handed as you say won't change the way the controls are laid out in the ships. You just have to get used to it like way you have to get used to the way the controls for a car are laid out.
You're most likely cross lateral. Many of us lefties are because there are no genes for left handedness, only right, and it depends which of the many right handed genes you have whether you're totally left, totally right, ambidextrous or cross lateral.
I use my left hand for writing, using a spoon and chopsticks (although I can use them in my right hand), everything else is right hand dominant. I'm left eye dominant but thanks to the A-Team shoot using my right eye (if I use a barrel red dot sight I see the left side of the barrel floating in front of me so I tend to use open red dot sights).
With pool/snooker neither way feels particularly natural, but I don't have to do that behind the back shot that righties do.
I'm a whiz at Jenga
Rejoice in having the best of both, the intelligence and problem solving skills that come with being a leftie, and the ease of using devices that are designed for a rightie!