Like could some trader in medieval France be selling a katana or urumi amongst his wares that he obtained in his travels? Could a merchant in Japan have a zweihander or flamberge in his collection?
Well, maybe not a katana, but if you count gunpowder, there is a fair bit of speculation that Chinese gunpowder weapons were used in Europe during the Mongol invasions.
Note that you'd have to research from there since it doesn't seem fully accepted that it actually happened, i.e. the Mongols might have only used gunpowder around China.
The other thing is that a katana might be a metallurgically brilliant sword, but I am unsure how it well it would perform in the hands of a European warrior, using local fencing techniques and facing other European warriors. There's a distinct lack of hand protection and Japanese close fighting did not seem to involve shields much. So it might not be treasured and valued, making notoriety, long distance trade and long term survival, of the weapon and its owner, unlikely.