According to the Trivia section, Brynner had already lost a lung to cancer before making "The King and I." Yet we see his bare upper torso often in the film, and I can't detect any sign of the significant scarring you'd have from chest surgery. Amazing!
Since Wikipedia sending wrong information and now people giving wrong info on IMDB. In his biography it said he had his lung removed in somewhere between 1984 and 1984. He after that surgery, my friend's mother was at his last Broadway revival in 1985 and she said he still had his chest exposed and it looked AMAZING. She also has the playbill program he autographed.
Yul's cancer was inoperable. He never had any surgery. There was a thought of removing surgically a tumor, but it was too near his heart. His treatment relied heavily on radiation.