Well, at best it'll only disable her a while. She won't die from the injection.
She might die from missing the race though.
From the demonstration we got in an earlier chapter, the poison is pretty lethal.
Maybe the moment she got pricked, she reacted by pulling away before the poison got injected, but if any got in her system, she's probably getting a trip to the hospital.
I can't really imagine just being immune to poisons as a solution to this predicament.
Alternatively, the guy might be a double agent, just pretending to be out to kill her but there's no poison in the syringe. He'd be there to raise her awareness as an assassin, even though she's already really good at being alert. Honestly, I'm surprised even this got past her considering how she was disabling the young assassins coming from behind. I guess she actually got flustered and didn't realise how strange it was for the old guy to be there; it wasn't anywhere near the race tracks nor any public restroom I think so why would he be there. I was confused about that, until he stabbed her with the syringe. I guess he had been tracking her too.
Someone in the previous chapter thread called it... I didn't think that would be the case at all. Thought her horse racing crew was too wholesome.
Maybe it's someone in disguise, with a mask and a great voice mimicry.