When I lived in LA, I played maybe a dozen times at Chester Washington, and me and a friend got paired up with 2 older golfers. One of them, a guy named Danny was 81, was tall and skinny with no real club head speed left, which was fine at CW really. He started off hitting driver left handed on hole 1, then when he was chipping I glanced and he was right handed and the same for putting. I was thinking, wait I thought he was a lefty?
He said he is a natural lefty, but couldn't find clubs left handed in his wedges / putter when he was young, so he found some right handed wedges/putter and has done it ever since. God bless him.