I'd go for the note on the door as well. Perhaps, indicate there's a cat inside as well. If you indicate 'do not open' only, it might incite curiosity ;)

It's gotta be stressful for Random. I remember when they re-carpeted the lobby in my apartment building. George 'the Lobby cat' threw up several times, and pooped a couple of times to show his displeasure. With the exception of that time, he NEVER has accidents in the building like that.