You might say that Artur Hawkwing just used it for a time. It was specially created for Lews Therin in the Age of Legends. So you might say the sword is really the Dragon's personal sword.
Possibly, sometimes there are errors in the artwork that make you think different things, so don't get too caught up in it. If I remember correctly, Callandor is shaped kinda like a long piece of crystal formation. The only actual sharp point to Callandor is the point. It doesn't have an...