By default, I think most historical leagues (say, before 1990) have injury settings that range from "extremely low" to "low." Keeping those settings should do a lot to cut down on injuries.
I've mentioned elsewhere that I don't think players in the "covered wagon days" got injured any less often than players do today, they just
played injured more often. When a player's entire career might hinge on whether he could show up to the ballpark that day, there was a pretty big incentive for players to suit up regardless of their physical condition. Wally Pipp, to take a famous example, woke up one morning with a stiff back and by that evening had lost his job to a kid named Lou Gehrig. So one way to duplicate the historical situation and avoid running out of players is to let players play injured instead of putting them on the injured list.
And if you haven't found it already, I recommend
Satchel's historical injury mod. It doesn't change the injuries, it just changes the descriptions to give them a more historical feel. So instead of a torn meniscus, for instance, the injury report will read something like "dead arm." Highly recommended
EDIT: I just realized that OOTP changed the injury model a little while ago, so Satchel's mod can't be used without modification. So that might be an interesting project if someone were so inclined.