Here is a list of teams, and the names of the players that have played at least one game, without playing enough games to qualify:

Cardinals - Clay Bouton
John Radzik
Bruce Whitman

Whiz Kids - Blaise Agnew

Dodgers - Greg Gougler

Damn Yankees - Greg Woolston

Cubs - Robert Coffey

I don't think that there are any surprises here, but this is the best way to handle this, so there won't be any arguments at game time.