That did not answer his question. The answer to his question is "no" you can not switch sticks in fallout 4. I agree with you Rpkstano as I posted a day ago. We're talking next gen here. Why button mapping but no stick options. Legacy and Southpaw options are as common today in AAA titles as are punkins are to halloween. Fortunately I have it on PS4 in which I can go into the system settings menu and switch the sticks. It's a hassle when having to switch it back to default when playing other games but at least I can play it this way. Just have to remember that the prompts to using L and R in the game are reversed when using this method.
Not to my knowledge. If they had, they would had incorperated it into Fallout 4 from the beginning without worrying about patching it later. If they don't fix this hopfully some modder will. But don't hold your breath.