Cadogan can't pretend not to have a phone. He very clearly does, and tends to take it out for typing to people who don't understand him right away. That doesn't mean he throws his number around willy-nilly, but hey, he's a friendly enough guy when you get to know him. His phone is able to receive:
TEXT, PIC TXT, CALL, EMAIL and VOICE MAIL
although (spoiler alert) he doesn't usually pick up calls. So drop him a line. Your friendly neighborhood smoke screen will pick up as long as he's not covered in finger paint, promise.