No, but the good news is that a sword can become a different sword once it's been crafted enough. Specifically, a sword at its third tier can become a different sword - there may even be like two options. I have a Cloud Zero sword, which isn't listed above because it was crafted from the Tiger Zero sword (possibly into King Tiger and then Cloud Zero). There was even another option that I could have picked instead of Cloud Zero when upgrading the Tiger Sword that I don't see above.
So, basically, pick the sword that has the priorities you like (sharpness vs length vs durability), and know that you can just keep upgrading it instead of holding out for another sword.