Link is supposed to be ambidextrous. They just made him a lefty in OoT for some reason.
It's the other way around. He was always supposed to be left-handed, but then they retconned him into being ambidextrous when they had to swap the stance around for the Wii motion controls in Twilight Princess. He winds up being right-handed in Skyward Sword and BotW for more or less the same reason.
He was left-handed in the Gamecube version of Twilight Princess and right-handed in the Wii version! Everything was mirrored in the Wii version (I think the sun set on the wrong side too?). But yeah, motion controls is pretty much why.