He is noted for being one of only three major-league players from Prince Edward Island, the others being 19th-century outfielder George Wood and catcher Henry Oxley.

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.

[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.

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.