Mafia Graves Can have a cigarette, but Graves can't have a cigar?

Thats a toothpick.

Default skins and default in-game models cannot have cigars (or likely cigarettes or pipes for that matter). Skins are outside the "core" game, and are fine, which is why Graves has a cigar in the A New Dawn cinematic and why Esq. Gragas can have a cigarette.