I have a question: has Zelda ever used a sword? I know she's made good use of a bow before, but I remember being surprised to see her with a sword in SMBC. I'd imagine that having Sheik use a knife wouldn't be any more surprising than having Zelda running around stabbing things, but I might very well have missed something. I'd also say that I'd think it would make the most sense if Sheik were a skin of Link, because it would effectively mean that Sheik is also a skin of Zelda, which seems quite fitting.
Twilight Princess. That's it. Having Sheik use a knife wouldn't be a problem indeed. But how could one make the sword look like a knife and have it as long as the swords? It would not forcefully look weird, but I'm not totally convinced.
Instead of a sword she could use the chain from Smash Bros (side B for those who never caught on that that was a chain (I only realized it when I read the manual for Melee)).