Teddy Roosevelt, at Putin's age, would have been a match. He loved to wrestle in the Oval Office.
He loved to shoot too, but was an average shot (at best). He boxed as well. I've heard he had an appreciation for jujutsu and sumo, had a lot of respect for the Japanese combat arts in general. Isoroku Yamamoto, of Pearl Harbor fame, got along well with Teddy. Gave him all kinds of pointers and info, not to mention a nice katana and lessons on how to care for it.
Teddy was scrappy, no argument there, but I'm not sure he's in the same class with long term martial arts fans like Putin or freaks of nature like Lincoln who would do prize fights and feats of strength.