Unfortunately wrestling isn't all that smart of a tactic in combat anyway especially without some sure fire way to kill that person in one hit.
also Shaolin monks had as many weapons as europeans and a few did use normal non farming implement weapons such as melon hammers, daos, and jian. But at that point in history the shaolin were contracted by the government, which ment they had to equip a field their monks with what ever money they were given. the monks, lacking armor beyond a simple wicker shield at most would rely on light weapons the lightest being their fists which proved deadlier than the slow fire guns of the untrained wokou who were ashigaru following low ranking bushi into exile.
Infact later on during the tokugawa shogunate buddhist monks slaughtered christian missionaries and converts disproving their care of their own religious strictures.
What im saying is that the monks deliberately nerfed themselves.
eitherway im getting away from the point, You see asia had long periods of peace allowing martial arts schools to become public, think of if Marines came back from iraq and began making money by opening MCMAP schools, This allowed martial arts to flourish and diversify.
so while you can pull out a few dozen units that had a distinct form of hug and punch it's so similar that it just known as medieval european martial arts. There is a reason why it died out, this is because IT WAS WEAPON BASED, when the weapons stopped being used the teaching of the martial arts stopped. the feats in D&D as presented showcase the martial arts as you describe without all of the specifics of weather or not their hand was opened or closed. The only reason other forms of wrestling survived is because they got absorbed into Greco-roman and became olympic sports or became cartoonish flanderizations of themselves made up comepletely one hit kill moves with no practicality what so ever.