So far we have already seen Link use a short sword, longsword, greatsword, several types of hammer, Magic wand, fire rod, ice rod, several kinds of magical arrows, whip, and a ball and chain. There is no shortage in the variety of weapons used throughout the series. Especially when things like bug catching nets and fishing rods can be used as weapons as well.
There have been a few varieties of swords used over the years. However I do not think a katana would be appropriate to the medieval setting of Hyrule. Link carrying twin swords also do not have that heroic knight appeal. Link was never really meant to be a ninja. However in Wind Waker Link was capable of using the various spears and longswords from Moblins and Darknuts. Even though the player could not keep them there was still a time when they were used.
If you are suggesting that a spear or axe be an alternative main weapon for Link to use then I do not think it would work. The standard boradsword and shield combination has that very heroic and iconic look for a legendary warrior or knight in this setting. Plus any other bladed weapon is not really needed when Link already has a broadsword to use. An axe would not be needed since there is nothing it cvan do that cannot already be done with a sword. A spear might be interesting as al alternative medium range weapon but it would require two hands to use leaving Link without a shield in his offhand. While it would not be any more powerful a weapon than a sword like the Biggoron sword, so there would be no extra benefit to having it other than simply having it.