Originally Posted by Super Jim
When I used the term "martial arts" I'm meaning "Samurai".
In fact, here is a definition:
Bushidō expanded and formalized the earlier code of the samurai, and stressed frugality, loyalty, mastery of martial arts, and honor to the death.
Since one of the things a Samurai puts first is his Lord, it could have been Yashida's hope that once trained Wolverine would feel some loyalty to Yashida, or maybe it could have been Yashida's attempt to keep Wolverine around long enough so he could take advantage.
Like others have said, there were all of these images of Wolverine with a Samurai sword, yet nothing. Yes he always ultimately needs to pop the claws and go bestial, but the fight could have started as a sword fight. Also, the whole term of ronin could have been developed more...
It still doesn't feel a natural progression to me that Wolverine would stick around and learn martial arts after rejecting Yashida's offer.
And for Wolverine to be an expert swordsman, good enough to go up against Shingen or anyone else for that matter, would be a stretch.
But I did think he might use a sword, perhaps once. I thought it might be how he killed Yashida at the end, but there would be no logical way for him to be holding the sword at that moment.