Shira attended college at Texas A&M University, where he played football as a tackle from 1943 to 1944. He received an appointment to attend the United States Military Academy, and was admitted as a Cadet in 1948. Shira played football for Army under Earl Blaik from 1949 to 1950. In 1950, he was named Army's most valuable player and to several All-America teams, including the International News Service first team. After the season, he appeared in the Blue–Gray Classic all-star game. Shira did not remain at West Point to graduate, however, and the following year, he served as an assistant coach at Tennessee before moving on to a position at Mississippi State in 1952. There, he worked alongside fellow assistant Darrell Royal under head coach Murray Warmath.