I guess you could put a piece of plastic/paper that covered with poison inside of straw.
If they drank it by using straw, the evident would disappear into dead body.
The culprit, the most likely, is the make-up artist.
The director is questionable too, From what he want to discuss like the culprit want.
but, It could be that culprit overheard that and want to know when he will able to talk.
But, you know, it could be multiple people.