A few possibilities for players with no cards:
1929 Dale Alexander -- RH 1B with the Tigers .343/.397/.580, 43 doubles, 15 triples, 25 homers (363 total bases), 137 rbis (rookie record until Ted Williams broke it) bulletproof (probably a 1L)
or
1932 Dale Alexander -- RH 1B with the Red Sox .367/.454/.513 (batting champ), 156 ops+, last great season for a player with .331 lifetime BA, in 1933 he was injured sliding into home and was brutally burned by the trainer who was using a new heat therapy. (probably a 3R)
1895 Jimmy Bannon -- RH OF with the Boston Braves .347/.417/.475, 35 doubles, 125 ops+
1922 Carson Bigbee -- LH OF with the Pirates .350/.405./.471, 29 doubles, 15 triples, 5 homers, 124 ops+ (probably a 4R or 5R)
1928 Del Bissonette -- LH 1B with the Dodgers .320/.396/.543 30 doubles, 13 triples, 25 homers (in his four-year career he had this triple double every year -- double figures in 2bs, 3bs, hrs) 145 ops+ the "Babe Ruth of Maine", probably would have had a great career if Dazzy Vance hadn't landed on his ankle during a volleyball game!
1894 Cupid Childs -- LH 2B with the Cleveland Spiders .353/.475/.459 123 ops+ (13-year career average 119 ops+)
2005 Tony Clark -- switch-hitting 1B with the Diamondbacks .304/.366/.636 154 ops+ (15-year veteran)
1895 Jack Clements -- LH C (lefthand thrower as well) with the Phillies .394/.446/.612 171 ops+ (17-year veteran)
1894 Lave Cross -- RH 3B/C (also SS/2B) with the Phillies .387/.424/.526 132 ops+ (21-year career average 100 ops+)
1980 Miguel Dilone -- Switch-hitting OF with the Indians .341/.375/.432 120 ops+, 30 doubles, 61 SB, 2R
http://365.strat-o-matic.com/player/833051/1680/1/802005 Mark Ellis -- RH 2B with the A's .316/.384/.477, 128 ops+, one of the greatest defensive 2b of all time
2005 Morgan Ensberg -- RH 3B with the Astros .283/.388/.557 144 ops+ 4th in MVP voting
2011 Adrian Gonzalez -- LH 1B with the Red Sox .338/.410/.548 155 ops+, led league in hits,
http://365.strat-o-matic.com/player/423/2011/1/20111895 Mike Griffin -- LH CF (plus SS) with the Brooklyn Grooms .332/.442/.454 139 ops+ (12-year career average 123 ops+) probably pretty decent in the field
1950 Johnny Groth -- RH CF with the Tigers .306/.407/.451 117 ops+ (15-year career average 99 ops+) 2L?
1927 George Harper -- LH RF with the Giants .331.435/.495 149 ops+ (11-year career average 118 ops+) 5R or 6R?
2000 Richard Hidalgo -- RH OF with the Astros .314/.391/.636 147 ops+, 42 doubles, 44 homers
2012 Torii Hunter -- RH RF with the Angels .313/.365/.451 129 ops+
http://365.strat-o-matic.com/player/545/2012/1/20121894 Bill Joyce -- LH 3B with Washington (NL) .355/.496/.648 178 ops+ (career ops+ 143), 25 doubles, 14 triples, 17 homers
1994 Mike Kingery -- LH OF with Colorado .349/.402/.532 126 ops+
http://365.strat-o-matic.com/player/36421/1690/1/901895 Bill Lange -- RH OF with Cubs .389/.456/.575 157 ops+ (career 123 ops+) highest single season batting average in Cubs history
1997 Ray Lankford -- LH CF with the Cards .295/.411/.585 159 ops+ (14-year average 123 ops+) 36 doubles, 31 homers
2004 Carlos Lee -- RH LF with the White Sox .305/.366/.525 127 ops+ (14-year average 113 ops+) 37 doubles, 31 homers
1900 Kip Selbach -- RH OF with Giants .337/.425/.461 149 ops+ (13-year career 121 ops+)
1896 Mike Smith -- LH OF with Pirates .362/.454/.500 155 ops+ (14-year career 126 ops+)
1899 Fred Tenney -- LH 1B with Braves .347/.411/.439 125 ops+, 17 triples, 17-year career
1896 Mike Tiernan -- LH OF with Giants .369/.452/.516 158 ops+ (13-year career 138 ops+) one of the more important Giant outfielders
1894 Tuck Turner -- switch-hitting OF with Phillies .418./458/.539 144 ops+, probably not that great in the field
1925 Al Wingo -- LH OF with Tigers .370/.456/.527 151 ops+ probably a 2L or 3L