Kid and vermouth are both good at disguising appearance-wise
Kid is good disguising his voice but I don't know how vermouth disguises her voice.
Vermouth is better at hiding her identity (copying every single action of a person) compared to kid.
Gosho Aoyama probably wants us to think Okiya is Bourbon, so he leaves behind deceiving hints like Okiya drinking bourbon or watching conan and haibara secretly.
This is so similar to the vermouth arc.