Fritzie Zivic had the right strategy..you would retreat behind a jab and counter, then occasionally stop short and flurry, then get out of the way again, reverting to fighting off the back foot. This exactly what Zivic himself said in an interview after his fighting days were over, and it was quite successful, and Zivic followed such a plan with conviction, as well as using his well known repetoire of dirty tricks in close just to keep Hank honest.
I don't think a Zivic equivalent at featherweight or lightweight could keep up with Armstrong, not in '37/'38. Nor would Armstrong cut as easily, or be affected by said fighter's power. Zivic practically blinded Armstrong, who suffered greatly because he couldn't see the punches coming.
I'd take Sandy Saddler at featherweight. Plan: Hold and hit with the uppercut (what else?) and take whatever comes your way because you're a tough sonofabitch.
I think this is essentially the blueprint. Boxers can cause Henry trouble his agression and sheer output would see most of them off. I'd go with Saddler, economical, numbing power and able to stalk and deliver accurately. He was also a hard man who can do it at range and close quarters.
I don't think that was all Zivic though. That was the last 2 or 3 years-worth of cumulated damage, that was never given time to heal because of Armstrong's hectic fight schedule. There was even some question over whether the commission would sanction their rematch in the first place because of all the damage to his eyes. After Armstrong took a year off and allowed his eyes to heal, they never were such an obvious factor in his fights again, and he was able to beat Zivic soundly in a third fight.
Roberto Duran at lightweight. I can't imagine anyone, welterweight and below, taking the fight to Duran and winning.