I can't recommend spending the $40 for the cleaners to possibly ruin it. I had a nice leather backpack that got a beer soaked bottom at a Jummy Buffett concert thanks to the idiots behind us. I didn't even know until I picked up my bag to leave :-(
The cleaners sent it back to me looking actually worse so I just wasted that money too.
Since it is "just" smoke I would try airing well, maybe some bounce sheets in pockets too. DH got a jacket from a friend that smoked and he hung it out in the shade for several days and it no longer smelled of smoke. Not sure I would want to use Febreeze or anything wet even on the lining due to spotting.