I was playing with my friend and we thought we could opt to use the fury to add a damage when we wanted to, but I just noticed that the Warrior's Katana omits the word "may".
It reads, "Once per turn, spend 2 fury to add +1 Damage to one of your Combat Hits."
Therefore, if you have 2 fury when you do your attack, you MUST use it to add a damage point to one of your hits.
It's optional. The imperative language that Brimstone uses on its Hero-friendly cards/abilities/upgrades can be misleading to newbies. Unless those things use the word "must" (usually in caps or italics), you can be reasonably sure the activation or use of said things is optional.
Note that this is not necessarily true of the text of things that don't represent some Hero asset, like Encounters or Darkness Cards or Missions themselves, whose text often omits the word "must" but is still phrased like a command. These are treated as such, because they come from the part of the game that IS imperative - the part that actually runs the game (rather than the part that describes what your Hero is capable of).