[Kalimac]

I'm out of town at the moment and so don't have my books with me, but I don't believe there's any statement that Narsil is the only weapon that Strider has. I'm not a swordswoman of any sort but would imagine that carrying two swords, one on each side, could get kind of awkward (unless you were ambidextrous) and carrying two on the same side would lead to obvious complications when you reached for one and accidentally grabbed the wrong hilt. So at a guess, Narsil is probably the only sword with him, which he carries for its power and symbolism. OTOH there was nothing to prevent him carrying long knives or a bow on his back, or possibly both. That would have made sense, especially since in his years in the wild, a lot of the threats/foes he met were as likely to be nonhuman as human. And if he was hunting for meat, a bow and knife would be much more useful than a sword of any kind.