Not necessarily a puncher, its a fightet that may fight out of Rhythm and is effective against the very skilled or atheltic Ken Norton did not have the best whiskers but he had a rhythm breaking style. He proved it against Ali,Young and Holmes. Marciano had a great chin and he proved his Rhythm breaking style vs many of the slickest. Jake Lamotta was one to a degree and Harry Greb was one of the best.Vitali Klitschko has those skills. Who else falls into the Rhythm breaker title both past and present.
Max Baer comes first to my mind. This trait of his was a key reason why many experts believed he would have had the best chance to upset Holmes, among Larry's predecessors as heavyweight champion. He had a crazed unpredictability well suited for breaking the mastery of control brought to the ring by a Holmes. He was good in rematches, avenging decision losses to Shaaf, Risko and Farr, also all on points, proving he wasn't wholly dependent on the knockout to win. (Nearly did take out Shaaf though, in a sort of preplay to Liston-Whitehurst II.)
This post has Harry Grebs name written all over it. Its all his opponents ever talked about. "He confuses you"
I considered Greb, but Harry did have some problems with master boxers Loughran and Mike Gibbons. (After first squaring off with the Phantom, Greb told his manager, "Next time, sign me up to fight just one guy.") Tunney also figured him out as their series progressed. As I said though, I did consider him, and it's a perfectly good answer.
Kid Gavillan was a master of syncopation who would establish a rhythm, impose it on the action, then punch inbetween the beats. Q: Does that make him a rhythm-breaker, or a rhythm-maker?
Ricardo Mayorga for all his limitations, could take a technically sound fighter out of his game. Frans Botha not bad either for a somewhat limited guy
The only rebroadcast of a complete Gavilan bout I ever watched was the kinescope of his match with Hector Constance, and he came across very much as a rhythm maker. (If you closed your eyes and just listened to the loud pop his bolo punches made on contact, you could virtually hear the beat. He used it almost like a jab, initiating action with it repeatedly.)