I dunno I feel Ren is more of a scrapper than he looks, kinda like Miguel in Tekken, he's a street fighter with brawling moves and no discipline but his brute strength and survivors will keeps him on par with the Kazuya's and Law's or you could compare Ren to Bronn from Game of Thrones, Bronn has no discipline but he is street wise and knows how to survive, I imagine Ren would be very similar to Bronn but yes definitely would get his ass whooped in a situation where he would be forced to fight with honor. Same reason Bronn avoided the fight with the mountain would be the same way Ren would avoid a fight with Lan Di.
TL.DR
Ren would kick Yamagashi's San's ass albiet unconventionally.