Right, as someone said you can be just a "Link", but we made it so ... it's not so Linky, you know? Link steals everyone's thunder every time.
But if you want to be a "look-a-like Link" you can become a Swordsman. They're probably the closest thing you can get to just a normal Link.
Oh by the way, I whipped up a guide. It should be along with the new OoL next patch.