That was Law. There was never any mystery to that at all except from people who confused the issue by insisting it must be Monet. (who was obviously secretly sweet and kind and knowingly letting chopper go so she could be the next crewmate.)
Since the very next chapter, a total of like 4 pages later, it was clarified that Law's chains weren't seastone and he had his powers, and the note appeared out of nowhere.
It's NOT a mystery.
Yes, I know that's the most reasonable explanation, but it still annoys me that there never was any absolutely clear confirmation of that.
I mean the way the sequence is staged is just really confusing. Sure, the weird look Monet gives when Chopper runs away doesn't help, but that's not even my main problem with the scene – we see Chopper receiving the note, and actually wondering out loud, well in a thought balloon, who threw it and were it came from.
Then in the next chapter we do realize that Law wasn't really wearing seastone chains, and is free to use his powers, but he does so only to explain how he could remove his shackles then. He doesn't mention that he has already used them previously while Vergo and Ceaser were still around to transport the note. Wouldn't they have noticed him using his room to do that, anyway? Or did he already have his chains removed and just threw the note himself. Well in that case the panel in which he appears, exactly before we see the note hit Chopper doesn't really indicate that. Actually it doesn't really indicate him doing anything…
I really don't care about Monet at all, but still thought that scene to be super irritating. Maybe it's totally clear through context and I am an idiot for not getting it, but usually Oda presents things in a way so even idiots get what the hell is going on. Like having one of these flashbacks with grey panel borders where the hero's plan is revealed in retrospective, like he had when he showed how Smoker got his heart back. That wasn't the case here. Chopper wonders who threw the note, so I wonder who threw it. Then we never get a real answer to that aside from context, which doesn't really make that much sense I think.
So I think it's a bit unfair to blame it entirely on fanboys that the scene caused irritation.
Anyways if Law's speech quirk was used on the note, that makes it a closed case. I just frankly didn't know that and am sorry for even bringing the issue up. Blame it on translation…