Jordan Peterson jokes aside, I think Schmidt will take this one. He was able to hold his own against Captain America after all (although that version of Steve didn't yet have the advanced martial arts training he would acquire later on).
By contrast, Alexei's only feats are winning a bunch of arm-wrestling contests, beating up Russian prison guards, and getting his *ss royally handed to him by Taskmaster, who Natasha performed better against. In fact, its unclear if he's ever even fought another super-soldier, given his tall-tales about beating up Captain America. However, it is worth remembering that this was Alexei after he had spent the best part of two decades rotting in a gulag and putting on weight. He also didn't have his shield (he clearly did have his own shield once, judging by his action figure). Its a shame we didn't get to see more of Alexei in his prime, but based on the version we got in Black Widow, I can't see him winning here.
Its also worth pointing out that while Alexei certainly has a ruthless side (praising Natasha and Yelena for the red in their ledgers), he's nowhere near as vicious or murderous as Schmidt, who's just a straight-up psychopath.
Red Skull wins.
Oh, and Docker, thanks for doing this match-up!