If I would have to guess I'd pick #2. But the different timelines one is scetchy AF.
1.) Hayate Amatsukami is the last remaining member of his clan.
2.) Hayate Amatsukami is left handed.
3.) Hayate Amatsukami's driving goal in life is to purge Akashima of curroption.
Answer: Hayate was originally left handed, but had to learn to become right handed after he lost his arm.