I handle the situation in one of three ways. I am extremely allergic to smoke. I can be bedridden for days if exposed to con centrated smoke.
If I with others they have no problem handling the problem for me. If I am alone, I always take the "I'm sure you didn't know" approach. I approach them and say I'm sure you didn;t realize this is a non-smoking park. I have ALL the smoking permitted areas committed to memory. If I have a brochure with me, (It's a good practice, you leave them with no excuses) I give it to them, so they can find the nearest one.
My third way was applied only after extreme rudeness on the part of the smoker. When parties in my group approached him and told him it was non-smoking, he said he'd smoke where he damn well got the urge. and right now it was right here. My friends continued to explain that I had ashtma and allergies and had been carried out of Disney parks on 4 separate occasions on a gurney by Reedy Creek due to smoking. (Ruined my day) The guy refused to put out the cigarette. I didn't have my inhaler that day and went close enough to ask him to stop. Thinking that if he could see the effect it was having he would be more considerate of others than himself. I was sure he would be sympathetic. No he reached out with the cigarette and said "here try it. It helps me when I feel out of breath". As I drew away he followed/chased me. (not that I could run, just the faster I walked, the faster he walked). Well that was the last straw. All EIGHT of us became very verbal. He was waiting for his wife to exit a restaurant so he really couldn't leave.
He said what are you going to do call Security on me? Well, it hadn't crossed my mind, but "Yeah I think I will". I keep their number stored in my cell phone. if you don't know it just store the main number 407-824-2222. They will patch you through to security in any area you request. When the CM Security Host answered the phone with his first name, I called him by name and told him the situation. He dispatched someone immediately. Well that scared the guy off. Once our CMSH showed up we expalined all that had happened and their first concern was for me. Once they were sure I was OK they reported the guy's stats over the radio. Heighth weight, clothes etc.
Several times that day a security host would approach me (must have given my stats too), ask if I was OK and gave me a "report". They said they had been tailing the guy as he crossed from area to area and NO ONE was allowing him to light up in an unauthorized area.
A bit extremem, but then again so is my reaction to cigarette smoke. ALWAYS point out the smoker to a CM. I have learned that smoking CM's do not 'SMELL" the smoke the way we do so they do not notice it. If you point it out to them they are almost always willing to assist. When they don't I ask them to call someone else who has been trained or feels comfortable approaching a violator.