Re: Most relaxed fighters in the ring.
Muhammad Ali was as chill a fighter as has ever boxed.
James Toney has no tension; He's perfectly calm. As has already been said, it is a huge part of his conditioning; He isn't in shape, but he burns ZERO excess energy in nerves.
Roy Jones was, and still is, steely calm in there. His reflexes are sharp, but a big reason they always looked other worldy is he had perfect attention while fighting; He was always present, never flustered.
Sugar Ray Leonard was the focused kind of calm. Watch his face and his body in his fight with Hearns, his greatest victory(Even over Hagler, imo): He's always watching Hearns, wasting few motions, just intent. It's rather impressive.