A quick check at Baseball Reference brought up a list of six Cubs that were born on June 4. I don't have cards of three of them:
Chang-Yong Lim, who pitched in six games in 2013
Lee Magee, 79 games with the 1919 Cubs
Orlie Weaver, 13 games with the 1910 and 1911 Cubs.
The three others with cards are: