The story modes never specified, but it is possible to speculate. If Okami is a Nox Nyctores and since Nine created all of them besides the Murakumo, it is possible he could fight using the claws on the hands and feet before he encountered her, but since Hakumen is Jin he likely fought with another sword because that was his preferred fighting style. There could be a timeloop paradox with the Susano'o armor and the Okami like there is with Ragna's sword and outfit where they are inherited from the past loop leaving the origin unknown or in Hakumen's case, having the Okami permanently stuck on his armor with each prior loop as well, but I believe it is more likely he fought with some generic sword until he obtained Okami. When he went back into the past, he could have still had Yukianesa to though and choose to abondon it when given the chance since he does try to distance himself from his old life, and by giving up Yukianesa when he could have Okami which also seems to have the better combat potential.