There seems to be some confusion over Leonardo’s swords. It seems that in the 90’s we were accustomed to thinking of his swords as Katanas, whereas more recently, his swords have been thought of as something else. This is largely because Leonardo’s swords have in fact changed.
The TMNT 1989 video game clearly had Leonardo wielding katanas
But later renditions, such as the 2007 TMNT movie and current Nickelodeon series that debuted in 2012 would begin showing him with straight swords (which according to Japanese history is more reminiscent of what a ninja would carry, whereas the Katanas were more of a samurai weapon).
Many of the newer renditions of Leonardo have him holding straight swords (definitely not katanas).
(Image courtesy of TeenageMutantNinjaTurtles.com).
TMNT 2014: Leonardo once again wields katanas
The 2014 TMNT movie once again has Leonardo wielding katanas. It’s worth noting that this is generally considering a two-handed sword, so the idea that one would run around with one in each hand may not make much sense. However, the 2014 movie version of the turtles generally tower over humans (maybe not Michaelangelo) so in this scenario, it would not seem as far-fetched given the sheer size of Leonardo’s hands.
So there you have it. The type of sword Leonardo wields seems confusing because different his different versions have been inconsistent in this regard. So as for as the 2014 reboot is concerned, they are katanas. As far as the current TMNT animated TV show, they are straight swords, perhaps ninjatos.