S.S.
My son is asthmatic and we have had to deal with this for a few years now. My father does not smoke in his house when we are visiting and I have no qualms with asking smokers to put out their cigarettes. I usually do it politely, but have been known to be kinda rude if they don't. I usually approach them and say, "Excuse me, but my son has really bad asthma and smoke sets it off, would you mind putting that out or smoking farther away from him?" It usually works.
If we are somewhere where smoking is prohibited, I will say, "Excuse me, but smoking is not allowed here." It usually gets them to put it out.
Honestly, my son's health is more important than a smoker feeling put out.