While he was enrolled at the University of Rio Grande, he attended a tryout camp for the Cincinnati Reds during the summer of 1985, where he received little attention.

[3] He rose through their farm system, reaching Double-A in 1988 with the Williamsport Bills and Triple-A in 1990 with the Colorado Springs Sky Sox.

[2] In November 1992, Shaw signed with the Kansas City Royals, who traded him the following month to the Montreal Expos in a multi-player deal.

[2] In August 1995, Montreal traded Shaw to the Chicago White Sox in exchange for pitcher José DeLeón.

[2] In January 1996, Shaw signed with the Cincinnati Reds,[2] allowing him to commute to the ballpark from his home in Washington Court House.

[8] Though he could have negotiated for a higher rate elsewhere, he was willing to sign a contract with the Reds at a discount since he could live at his home in Washington Court House.

[8] Shaw's agent stated they asked Reds general manager Jim Bowden for a no-trade clause, but he would not agree to one.