It's a HUGE no-no...I smoke, I have smoked since I was 21, and I'm now 38 and have ALWAYS owned multiple parrots, and I have NEVER ONCE smoked a cigarette inside my home/apartment. I put on a hoodie before I walk outside, walk outside to smoke, then I come in and immediately take off the hoodie, wash my hands with antibacterial soap, and don't go anywhere near the birds until I do...
Honestly I can't imagine actually smoking inside my house, not anywhere inside my house, and I don't say that to be rude to you, I say it because you are lucky enough to own a Cockatoo and it shocks me that you would even think about doing so.
You have to remember something very important, and that is that you are thinking of smoking/second-hand smoke in terms of how it effects humans and attaches to human's clothing, etc., BUT YOU ABSOLUTELY CANNOT COMPARE BIRDS TO HUMANS WHEN IT COMES TO ANY TYPE OF SMOKE, FUMES, ETC.
Birds have such a complicated and important respiratory/air sac system throughout their bodies that it effects everything they do. Think about it this way: A PERSON CAN COOK USING TEFLON PANS IN THEIR KITCHEN, WITH THEIR PARROT IN ANOTHER ROOM WITH THE DOOR SHUT, AND THE PARROT WILL OFTEN STILL DROP OVER DEAD FROM THE TEFLON FUMES...Think about that for a minute and then ask yourself whether or not you think that if you smoke a cigar in your bedroom with the door shut, your Cockatoo will not only be able to smell it WHILE YOU'RE SMOKING IT, but forever afterwards, not only in the air, but on you, on everything...
In my opinion you are greatly risking the life/shortening the life of your Cockatoo if you make the decision to smoke ANYTHING inside your home, anywhere in your home, as they will be breathing-in those molecules all day and all night, every day, forever unless you do a deep clean throughout the house. That's the scientific truth, you can read several journal articles stating as much if you Google it...
You have a Cockatoo, you have a responsibility. Please, never ever smoke anything, not a cigar, a cigarette, a spliff, etc. inside your home anywhere. I know you "want" to smoke cigars in your bedroom, but you have a parrot that relies upon you to take care of him for decades and decades, so you can't always do what you "want" to do...Go outside to smoke your cigars please...And just so you know, I live in central Pennsylvania, so smoking outside in the winter is a *****, but I do it, because I made the choice to have birds, so if I want to smoke I have to do it outside of my house. End of story.