Back in the earlier days (before players got bargaining strength for salaries through a union), most players had to work in the off-season and a lot of them reported to spring training out of shape, Today, players can afford to spend time off-season to train and home skills, to study video tape and things. In general, parks were much larger* so players weren't trying to hit home runs with every swing; therefore, pitching strategy was different and starters weren't trying to throw every pitch as hard as they could. They went deeper into games and still had their fastball when needed. [There was no way of accurately measuring pitch speed but there certainly were pitchers who could "bring it" and who undoubtedly could have improved their speed given today's techniques, training, etc.]
Batters back then didn't have the ways to improve eyesight that today's batters do--Lasik surgery, contact lenses, eye training methods--but there certainly were players whose instincts, reflexes rivaled today's players. And they didn't have the video tape and data on pitchers to study.
*The Red Sox began playing in Huntington Avenue baseball grounds: CF was 530' until it was extended to 635' in 1908. The original Fenway Park had a 324' LF/488' CF (with a deep niche of 510')/405' RF power alley/313' RF. However, the RF line went to ~358' from 1926-30, 1933-35. There was a reduction in LF (312')/CF (388.7')/CF deep niche (420')/RF power alley (382') in 1934. Also, the addition of seats in RF reduced to distance for Ted Williams in 1940 in the power alley and down the line. Fenway was by no means the only park to have vast distances to the fences compared to today's stafia.
All-in-all, you are talking about a different ball game and if the players of yore were given the chance to train and study with today's improved methods and they played in today's parks, I think a fair number of them would succeed.