The fallback position, if programing remappable keys is just not an option in your title, is alternative configuration setups. The idea is simple: develop predefined controller configurations that allow a gamer to select one that best matches their play style, and their disability.
Conventional console developing logic requires including both normal configuration, southpaw, reverse and a few random layouts as a catchall. In order to be truly accessible the configurations must include right-handed, left-handed, button combinations near each other and one-handed.
Developer Exercise: Take a look at the controller, and see if you can play your game with one hand. Place the controller on your knee, your desk, or your thigh and give it a go. If your game is not at least semi-playable with one hand and you are not pleased with the results, alternative configurations can be a reasonable fix if fully remappable keys are not an option.
An example of multiple configurations being done properly is in Halo Reach by Bungie. They have six out-of-the-box configurations, such as BOXER, GREEN THUMB, and BUMPER JUMPER. They also thought about those gamers who are left handed by including a SOUTHPAW configuration. While this may seem to be a luxury, when a disability determines what buttons are easy to press and which ones cause fatigue, it is imperative that the disabled gamer be allowed to choose the path of least resistance and maximum enjoyment.