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And there it is, though you can’t quite see all of it: Needle. Arya’s right hand is pull the scabbard and belt away, while holding the hilt with her left hand. You can faintly see the hilt, which we also saw here in the Artisans video focused on weapons.
As we’ve noted previously, this is very much a smallsword-style weapon, though GRRM notes that Braavosi waterdancer’s swords aren’t all that rapier-like at all, but are rather more like more slender versions of the Westerosi blades. Needle in particular, having been forged by the smith at Winterfell, is supposed to look very like a slimmed-down knight’s sword made for a young girl.