Dillon, 34, appeared in 15 games for Tampa Bay last season as a designated hitter, third baseman and second baseman, hitting .300 with one home run and two RBIs. He was a member of the Rays' active roster for 62 games May 26-Aug. 7.
In 35 games for Triple-A Durham, Dillon hit .244 and spent time at all four infield positions.
Dillon was acquired from the Athletics on May 9 as the player to be named in exchange for infielder Adam Kennedy. He owns a career .263 batting average over parts of four Major League seasons with the Marlins ('05), Brewers (2007-08) and Rays ('09).
Shealy, 30, hit .345 with seven doubles, 12 RBIs, 18 walks and a .454 on-base percentage for Triple-A Omaha in 2009, but he did not play after May 8 due to a knee injury. Shealy has played parts of four seasons in the Major Leagues with the Rockies (2005-06) and Royals (2006-08), hitting a combined .271 with 19 homers, and 94 RBIs in 164 games. Over parts of eight Minor League seasons, he owns a .311 average with 132 homers runs, a .401 on-base percentage and a .564 slugging percentage.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.