Well, unless you are RP-ing that the katana's are stuck to your hand, there's no reason your character can't carry one of the more common fire-dealing weapons. He may train with katanas, fight with katanas, and eat with katanas, but if they will not get the trolls killed and your character knows that, it'd be stupid to fight trolls without posessing something to finish them off.
It's not going out of character if you use a club only for that nasty job, and in fact the penalties you get when wielding one are there to represent that you do not really know how to use it.
An alternative would be to use potions that deal fire damage, like the potion of firebreath or the oil of fiery burning.
Also, didn't the gnoll from the cloak of the sewers have a firedamage-dealing halberd?
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