Could prestidigitation be used to clean poison off an enemy's arrow?

[Zhorn]

One substance coating an object? That's as close a definition to soiled I can think of without rules lawyering to weasel around it. Check
Target within range? 10 feet as per the spell text, so; check
Object in possession by another creature? Spell text makes no such restriction, so I see no reason to disallow it. another check

At this point I'm incline to view this as a perfectly acceptable use of the spell. If anything I think the question would change from "could this be done" to "what houserule do you foresee DMs attempting to block this with"

such as

I'd 100% allow it, and just treat it like any other spell allowing a dex saving throw.

OOh, yeah, like the save versus Light Cantrip. (Which I have used in combat!)

which to be fair sounds reasonable enough on its own, but when you have a DM doing this for every outside the box idea even when you're still colouring inside the lines, it can become very frustrating and turns from "let's see if this creative spell use works" to "here's an extra hurdle to make it less likely to work" (been a player in that game. not fun).
At least for the basing it off the light cantrip feels like a similar power scope, though for light the dex save is for avoiding a touch.
For a spell affecting an object in another creature's possession but not manipulating the object away from them, I'd be more inclined to view this as heat metal; the spell just lands on the object without a save.