Wedge played catcher for Wichita State University from 1987–1989, leading the school to a 68-16 record and the College World Series championship in 1989. He hit .380 for the Shockers that year, led the NCAA in walks and total bases and finished second in runs, RBI, and home runs. Wedge's performance earned him first-team All-America honors, the Missouri Valley Conference Player of the Year award and he was runner-up to Ben McDonald for the Rotary Smith Award for College Baseball Player of the Year.