Probably. Does that ability of yours allow you to control the size and shape of the sword? cause, if so, then you could find a type you like and then get a permanent one from the shop. It won't be special to start, but you can make it special... like this...

[ sets her hand just under the carving on the hilt and smiles. ]

Falcon, huh, I like it. I wonder if I should name my sword.