The demonstrator and killer are NOT the same person, due to an earlier statement.
Possible candidates: Kisume, Kogasa, Satori/Koishi, Letty, Murasa, Komachi(?), Shiki(?), Nitori, Nue, Suika, and Yuugi. Or do I have the conditions too wide/narrow?
So that would be... Kisume, Kogasa, Komachi, Nue, Suika, and Yuugi without hats, and Satori, Koishi, Murasa, Shiki, and Nitori with hats. Huh, roughly even split.
I'm guessing Satori was the demonstrator, and discovered the killer through demonstrating her powers?