Okay, I can give you some advice on avoiding second-hand smoke on the Pearl. Finished a cruise on it just 9 days ago. I too am very allergic to cigarette smoke.
My trick to avoid the casino to get to the theater shows: use a forward elevator from any floor except deck 6 (where the casino is) and go to deck 7. Enter and exit the theater from the top on deck 7.
Avoid deck 13 above the pool area. There is a bar on 13 that overlooks the pools on deck 12. I didn't find any mention on NCL's website of this bar being a smoking area, but it was. I try very hard to completely avoid the smoking areas. The line, indeed all cruise lines, should have a page with more specific info on this matter.
Now, here is my real beef re: the cruise I just took and the casino. One morning all passengers had to report to a particular restaurant for a customs check. The crew ordered us only to use a particular route to get to it and chained off or otherwise barricaded numerous corridors, forcing everyone to go in one long, snaking line. Guess what place it passed through? You guessed right, C-A-S-I-N-O. Thank God I wore a mask! Now, the casino was closed that morning and no one was smoking in it, but still, a casino that allows smoking every night is going to have second-hand smoke residue. Okay, I understand why they have smoking in their casinos. I just choose to stay out of them. But, NCL, you should not be FORCING people to pass through them to get to other places on the ship..