Interesting discussion here...
Unarmed hand-to-hand combat is naturally the oldest form of fighting, and techniques to improve its efficiency stretch back to antiquity. Eventually skills first taught for warfare became the basis of competitive sports, such as Greco-Roman wrestling. (In fact, most if not all of the ancient Olympic games had martial origins -- discus, javelin throw, etc.)
Krypton was probably no different during its early history, as we've seen stories of primative Kryptonian tribes fighting among each other and against technologically-superior alien invaders. The ancestors of Klurkor and Horu-Kanu might have been developed during this time, perhaps under circumstances similar to Okinawa, as JulianPerez pointed out -- the ban on weaponry did not extend to everyday items and farming tools, so a simple walking stick became the "bo", and the rice flail shorted into "nunchaku". One could imagine "The Headband Warriors of Krypton!" (
https://www.supermanthroughtheages.com/tales2/headband/) also resorting to martial arts.
As Krypton became more civilized, traditional unarmed fighting might have waned as a combat skill but was retained as a competitive sport and a means to promote physical fitness and (according to many Chinese-based martial arts) spiritual well-being. And then there were personal protection issues -- Krypton still had crime, but weaponry carried by private civilians seems to be rare. Perhaps Kryptonian society frowned on this "barbaric" practice (betraying a lack of trust in fellow Kryptonians), or perhaps personal weapons were restricted by law. But Klurklor might have been allowed as an acceptable means of self-defense. (The more-lethal Horu-Kanu was probably another matter altogether.)
I suspect Horu-Kanu was a more combat-oriented martial art, designed to take down opponents quickly and decisively. It was designed to hurt, disable and kill, so it was either taught only to military and law-enforcement personnel, or banned completely. Kluklor might have been modified to stress non-violence, such as judo is a "gentler" form of ju-jutsu without the latter's striking moves, while aikido is purely defensive in nature. On Krypton, both Horu-Kanu and Kluklor were probably no more devastating than their martial arts counterparts on Earth. But a yellow sun-charged Horu-Kanu master like Faora Hu-Ul would be a dire threat.
It's interesting that Kryptonian physiology was so similar to Earthlings that Kluklor blocks, nerve locks, striking blows and throws could be used on both species without modification. You'd think there would be differences in nevre bundle locations, or the range in motion of some body joints. Lois Lane was probably so effective in Kluklor because her moves might not have resembled conventional Earth martial arts, so this confusion probably gave her the element of surprise. However, a martial arts master might begin to decipher Lois' techniques after intense observation, so that advantage tends to vanish in a prolonged fight.
I suspect that since Kluklor is so rarely practiced on Earth, one might even throw Superman... ONCE. But after he gets over his initial surprise, you'll never get a second chance before he ties you up like a pretzel! :wink: