Handrahan threw right-handed, batted left-handed, and was listed as 6 feet 2 inches (1.88 m) tall and 185 pounds (84 kg). He was originally signed by the Milwaukee Braves as a 22-year-old amateur in 1959. After playing sandlot and youth baseball in his native Charlottetown, then pitching in a semi-professional league for Stellarton, Nova Scotia, in the heart of that province's coal mining country, he was signed by veteran Braves scout Lucius "Jeff" Jones,[3][4] whose territory encompassed New England and Atlantic Canada.
Handrahan spent four years at the lower levels of the Braves' farm system before the Athletics selected him in the 1962 minor league draft. He made the Kansas City roster out of spring training in 1964, and worked in 18 games between April 14 and June 9. Sent to Triple-A, he didn't return to the majors until Kansas City recalled him in the middle of 1966 for a 16-game audition. Handrahan made two starts for the Athletics, one in 1964 and the other in 1966, and they resulted in both of his MLB decisions: defeats at the hands of the Los Angeles Angels on May 5, 1964,[5] and the Chicago White Sox on April 17, 1966.[6] He earned his only major-league save in his penultimate MLB appearance when he worked a scoreless one-third of an inning against the Cleveland Indians to complete a 1–0 Kansas City triumph on September 15, 1966.[7]
Handrahan was elected to the Prince Edward Island Sports Hall of Fame in its first year, 1968, but could not attend the induction ceremony because he was pitching across the country for the Triple-A Vancouver Mounties at the time.[3]