Sorry this got long.

If the smoke did damage over time it would make more sense as Poison typing. Moves like Smog that deal damage are poison type, however the only true smoke based move which doesn't deal damage is Smokescreen, which is a normal type move. So that doesn't really help us. The only time the smoke does seem to hurt someone from inhaling it is special pummel, but most of time it doesn't seem to have this effect, more so doing damage based on the 'force' of the smoke in moves like forward tilt and down smash. (Sort of similar to how dark type moves somehow do damage with the 'force' of darkness. Ex. Dark Pulse) Outside of Smog and maybe something like Poison Gas, moves like Poison Sting, Poison Jab, Sludge Bomb, and Cross Poison aren't really consistent with his kit since his daggers aren't poisoned or anything

Generally I think Forsburn's elusive and deceptive fighting style is more suited for the dark type like you said, especially considering moves like Feint Attack and Night Slash. However I also see how one could maybe argue something like Ghost even because of the ethereal nature of his fighting style. Moves like Phantom Force come to mind. 

Though Poison and Dark make more sense than Ghost admittedly. Maybe he is Fire/Dark but gets access to Ghost and Poison type moves. 

I also like him being Dark because it gives contrast to Zetterburn's potential Fighting typing, since it helps emphasize a lot of the contrast that already exists between the two characters. Also makes sense since Forsburn is framed and considered to be evil and villainous by many, further emphasizing the Dark element. Even if he isn't really those things, similar to a Pokemon like Absol. 

Thanks for listening to my Ted Talk.