We've been having this headscratcher for quite a long time...
What kind of swords does Hylian Infantry use?
I suggest not to take into account their description pics, as they might be outdated or inaccurate, but rather their in-game models. (Also, do Hylian Knights have slightly longer swords or is it just me?)
A theory is that they're just One-Handed Swords wielded with two hands (apparently it's a tecnique to pierce throught armour, but it's not like Hyrule has many armoured opponents).
Or they might be Bastard Swords, which is a sort of in-between for One and Two-handed swords.
Or Longswords, or Claymores (the latter has an hilt slightly inclined forward like theirs).
Greatswords are an unlikely theory, as HI's swords are not much wide.
I'd support a Bastard Sword or Claymore.