You should quit for lots of reasons ! But I checked Snopes , and though they made no specific mention to player's , I quote:
"Menthols are rumored to contain fiberglass. According to this canard, the evil cigarette companies secrete the substance in the product in an effort to better transmit that menthol sensation and nicotine kick by way of causing tiny cuts in the smoker's throat and mouth. This same rumor also attaches to smokeless (chewing) tobacco, especially to the Kodiak brand.
There's no fiberglass in cigarettes. Granted RJR did try using a fiberglass shell on its flopped smokeless cigarettes in 1994, but that part of the contraption wasn't ingested by the smoker; it was more of a housing, if you will. Other than that, no fiberglass. "