The whole reason they tell you not to smoke after a tooth extraction is that no matter how gently you pull/draw that fragile clot in there that keeps you from bleeding and lets you heal can easily be dislodged. It may no longer bleed but you can more easily get an infection from any particles in your mouth lodging in the open site that the clot was acting like a bandage/filler.
That same smoking rule, since the mechanics are the same, would go for anything you essentially 'pulled' on. And its does not take much. They don't tell you to gently smoke or gently suck fluids in a straw and I doubt vaping would be any difference. The act of drawing is is enough to dislodge that clot during the first 24 hours. I had one taken out and when he said no smoking I told him that's was okay I vaped anyway. He gave me a very odd look and since he knew what vaping was I though 'oh wow he is going to tell me he vapes too'. Instead I got a lecture on the fact that I might not be breathing in all the crap from a cigarette but the mechanics were the same as smoking and I should not even consider it. Spent the day with the old nicotine patch (could not chew gum either). I guess if you vape somehow by just breathing the vapor and not pulling or drawing the vapor in like an analog it might be different but I don't know anyone that vapes like that :0
You got the best advice from face Meat, though, and that is to call and ask your dentist if you are not sure. Different dentists can have different cans and can'ts after they do work and they should have the say in what they want you not to do. You may even have to explain to him what vaping is and what your draw is like and then let him make the call.
If you can't reach him for an answer I would just abide by what your post-extractions instructions said about smoking.
