Stecchi was a three-year starter for the Crusader football team on both sides of the ball, playing tight end and defensive end. He led Holy Cross to an overall record of 16-9-2 from 1956-1958, including two victories over both Boston College and Syracuse. During his senior season, Stecchi led the team with 19 receptions for 331 yards and two touchdowns. He was named first team All-East and second team All-New England as a senior, after being selected first team All-New England as a junior. In addition, Stecchi received Catholic All-America honors from Extension Magazine following his sophomore season. Over the course of his Holy Cross career, he totaled 41 receptions for 687 yards and four touchdowns. Stecchi was also a member of the Crusader track and field team, competing in the high hurdles.