Is it tied to the job? The ability set? The item class? All of them?
I'm not sure how to go about reclassing the items since I'm uncertain as to if the katanas have to remain katanas in order for it to work or not.
I can't answer all of this but I do know you can change the weapons' type in FFTP and have it still be effective, which seems to reflect that the skillslots are tied to the items. For example, I've changed all of the Katanas to Instrument type weapons and they still called the skills in 4C-55 normally. The major difference being that the change in weapon type is going to change what graphics are called the skill is used if you stick to the vanilla sprite animations for those skills [holding the sword up may instead be a jumble of pixels held over the unit's head.]
http://ffhacktics.com/wiki/Draw_Out
http://ffhacktics.com/wiki/Katana_Break_Chance
http://ffhacktics.com/wiki/Katana_Inventory
I don't see that in any of these disassemblies but I think I read that someone changed that for a patch. Maybe it's in choto's big list of routines.
http://ffhacktics.com/smf/index.php?topic=9608.0