I am sure that Anthony Joshua, would be polite to somebody, who was employing him as a sparring partner!
In the instance of the old world all the best may have been working as construction workers. The risk to gamble on a boxing career was something that took beach ball nuts IMO back in "The good ol days"
With a ton of luck: Joshua trains some halfway decent fighters with modern training protocols (plus he's no slouch technically, and might have an edge over 20s-30s fighters in that department even in their own environment.) From the late 30s onward, he manages to become a modest, Blackburn-esque success at producing quality fighters. In part because he acquires early, legal PEDs to give to his fighters, combined with knowledge of how to use them. (Assuming he can get funding, which will be a chore, but not insurmountable. He knows how to project a fake, marketable persona.) He might not lose everything in the Great Depression if he remembers his high school history lessons. Joshua's influence brings PEDs into boxing in a major way decades before Spinks/Holmes might have done it. There may be a scandal or two about their use by the 1960s, since the Mob will be involved in boxing by then, so steroid use in boxing will be even more seedy than usual. Joshua's ultimate legacy is mixed. But many boxing historians put his behavior in context because he lived in a time that seriously limited his options. On the plus side, he was a decent heavyweight and an excellent trainer/conditioner of heavyweights. Wilder does none of these things, because he is not savvy, and probably lacks any valuable future knowledge he could exploit.
I'm not saying Joshua invents them. I think he brings them in after they're invented by other people. Too late for his own career, but not for the fighters he trains.
They are starting 0-0 in this case so they start destroying journeymen. Probably looked at as something akin to freakshows. I doubt they get a title shot in the 1920s based on the politics at the time. How would they hold up fighting every 2-3 weeks, no PEDs, with their diets going south quick? They probably will have to fight injured and with little money and they will probably have to work a hard manual labor job full time to start out with in a different era. Eventually other heavyweights and trainers of the day are going to start picking up on both of their bad habits/weaknesses as well and try to exploit them. Wilder is also going to be 37 this year, theres a lot of ground for him to cover to become an established threat before hes completely shot, and this 1920s schedule is going to do him no favors. Is Joshua cut out on doing this type of lifestyle under these conditions for another 5 years?
If we sent AJ as we know him back in time and put him against the likes of Bob Fitzsimmons, Tom Sharkey and Jim Corbett, he would absolutely destroy them. Especially with those horse hair gloves. Ditto for Wilder. I can see the newspaper headline now the day after the fight: January 5, 1922 "Large, muscular negro decapitates opponent in ring. Officials investigate mismatch"
Assuming that they are sent back in their 21st century renditions then I think they would do very well with the size and power they have. While neither one is a master of the sweet science in terms of skill, they’re skills wouldn’t necessary be inferior to that of people like Willard or Firpo.
Is Frank Bruno v Bill Sharkey still on Youtube ? The answer can be found here. Brave little micro-Cruiserweight Bill wades out of his corner winging hooks. He is pushed forcibly backwards and knocked spark out by a single blow.