I think ThePuck nailed it. It's all going to depend on the conditions and equipment they maintain. Obvious comparison would be to something like an exposed element space heater. Is equipment and electrical stuff required to be certified for use in a flammable environment? I'm assuming it's not that rigid or they would have requirements like no shoes/boots with nailed soles, etc.
1) will be the technical aspects of your e-cig
2) will be the "smoking" and disruption aspects of you appearing to be smoking on the floor. If you are union let them do the talking and negotiations. If you're not, I'd play dumb and condescending. "It's just vapor and I thought it would be ok". "Umm, no, now that you ask, I never even thought about how the thing works but I'll find out". Get it continued and go from there based on their response.
If I had to wager (without knowing anything about your plant) I'd say that if you go into the initial meeting on the offensive you're going to lose big time.