Ken Silvestri made his debut with the White Sox in '39:
http://en.wikipedia.org/wiki/Ken_Silvestri
Vic Frazier played for the Boston Bess in '37:
http://en.wikipedia.org/wiki/Vic_Frazier
Walt "Kirby" Higbe played for the Cubs in '37
http://en.wikipedia.org/wiki/Kirby_Higbe
"Gus" Cherry and Henry "Hank" Meyer played in the Cubs minor league system in '37
http://www.baseball-reference.com/mi...=CHC&year=1937