Games aren't specifically right or left handed.
What sort of options would you want to give us an idea of what you're looking for? Since the controller itself is set in stone and nothing is going to swap the physical positions of the buttons, I can't think of much that could be done.
I suppose the movement & aiming functions could be swapped for a first person shooter so the right stick moves and the left aims? But I don't see why anyone would want that. Same with movement and camera controls being swapped in other genres or ignoring the left analog or d-pad entirely and just using the right analog.
Ironically, many classic gamers consider gamepads to be almost designed for lefties. Early arcade games before the early 1980's and home consoles before the NES usually relied on using your right hand for movement functions. Despite a gamepad being a completely different type of game controller, using their left hand for movement still gives a small minority issues these days if you visit somewhere like the AtariAge forums.
To me, the left analog stick, d-pad, and left trigger and bumper are just as important as the control functions on the right hand side. So at least for my hands (I'm right handed), I don't see any preference beyond wanting it to stay to what I've grown used to.