Doesn't fit in the game world? The lore says what fits, not any preconceptions carried over from Earth to Nirn. Akavir did invade, they left traces of their passing, and some of their traditions were perpetuated by the Blades.
Yes, you're right there, but you have to admit that being a tall blond-haired no-nonsense Nord wielding a katana in the cold icy mountains seems to be a bit.. strange..
However, according to the lore it would be appropriate.
And if you do not choose to be the blond-haired no-nonsense Nord the Asian styled weapons could look pretty good on your character. For example: a katana looks great on a battlemage imo.
Edit: a katana looks even better ripped through the heart of a battlemage..