1948 Joe Louis vs prime Jerry Quarry

Doubt it, Louis still had the jab and counter timing to give Walcott problems, a guy much faster and more skilled than Quarry.
Without the backtracking and the feints, Quarry's face becomes a target for straight lefts. He either gets stopped on cuts or tries to beat Louis to the punch and gets blown out in Maurielo fashion.
1948 Louis still had combos and hand speed.

 

No arguments there, any version of pre war Louis takes care of Jersey Joe but not without problems and possible knock-downs. However that doesn't mean the version who fought Walcott was shot.
Shot fighters don't blast out number 1 contenders in the opening round.

 

But very reduced speed and overall reflexes, I think you can argue Quarry being faster at that stage. His hand speed and timing against Frazier was very good, not to mention he kept up with Joe’s pace and even got the better of him on the inside a lot of the time with his speed. I could see him getting the better of Joe until Louis catches him devastatingly like he did Walcott. As you said it likely happens earlier due to Quarry’s willingness to exchange and get hit.
Still though, wasn’t Louis around 211-214 against Walcott? That probably took some of his speed as well, though he still had fast hands at that stage his legs were just beginning to fade.

 

Quarry's success against Frazier came largely due to Frazier being a close range slugger which allowed Quarry to exchange some punches before the trades went overwhelmingly in Frazier's favour. Louis has a sniper of a jab and two handed power to keep Quarry at bay.
As for his leg speed, yeah he wasn't as explosive as before but if he could corner Jersey Joe he shouldn't have issues keeping up with Quarry.
For what is worth, Jerry could come out fast and score a knockdown in the first, though I don't think that'd be enough to have him ahead on points if the stoppage came in the 4th or 5th round.

 

It’s clear as day, Louis was past his prime against Walcott…. Like it’s not even up for debate.

 

The past prime Joe Louis of the Jersey Joe Walcott fight still stops Jerry Quarry. Against this version of Joe, Jerry might look okay for a few rounds, but not too many.