The Yuan-Ti already has the arrow ready to fire. If I were playing the Yuan-Ti, I'd fire the arrow, mildly annoyed at losing the poison, then draw another envenomed arrow for the next shot. Seems most logical/reasonable.
Noticing the suddenly-clean arrowhead shouldn't be hard. The tip of the arrow is in the middle of their field of vision as they go to fire.
Saving throw feels applicable, as it is a carried item and you are getting a combat effect from a spell. All of the damaging/controlling spells generally give a saving throw or require a roll to hit.