Shaunessy was chosen 192nd overall by the Quebec Nordiques in the 1983 NHL Entry Draft out of high school, He played college hockey for the Boston University Terriers from 1983 to 1987. After the 1986-87 college season was finished, he played 3 games for the Nordiques.
In 1987-88 he turned pro with the Fredericton Express. The following season he played for the Halifax Citadels and was called up to the Nordiques for another four games. In the total of seven NHL games Shaunessy was scoreless.
Halfway into the 1989-90 season Shaunessy left the Citadels for the Fort Wayne Komets of the International Hockey League (IHL). He played in the IHL until 1993, when a back injury forced his retirement.
In 1996 he signed as a free agent with the Austin Ice Bats of the Western Professional Hockey League and played a season there. Shaunessy then played in 1997-98 and 1998-99 with other teams in the same league. He retired in 1999.