If you click on the image in the ebay listing for this picture, a series of pictures showing what appears to be the same "hat guy" in each image posing with multiple other Yankee players is there.
http://s1187.photobucket.com/user/kr...CKLE9.jpg.html
The player in question appears to be slightly taller than the "hat guy". If you look at the last image, it appears to be Ralph Branca, and at 6-3, he appears just slightly taller than the player in question (as compared to the hat guy). If it is indeed Branca, I would estimate the "hat guy" to be 6-1 or so. So, the player in question should be at least 6-0, thus excluding the "shorter" Yankees such as Berra, Silvera, and the others under 6-0.
My pick is Dr. Bobby Brown (at 6-1)
http://sportsillustrated.cnn.com/bas...s/1951_lg.html