A graduate of Chicago's St. Rita High School, Gapski attended Daley Junior College before receiving an undergraduate degree in physical education with honors from the University of Illinois-Chicago in 1982. He stayed at UIC for five years, serving as assistant athletic trainer for three years and head trainer for the final two years. While at UIC he provided athletic healthcare coverage for all of the Flames sports teams, and in 2011 UIC awarded him a Lifetime Achievement Award. Gapski was honored to serve as athletic trainer for the 1991 and 2003 NHL All-Star Games and for Team Canada at the 1991 Canada Cup.
Gapski, who was inducted into the St. Rita High School Hall of Fame in April 2015, is a certified member of the National Athletic Trainers' Association. His hobbies include cooking and gardening. Gapski and his wife, Lynne, have four children: Michael, Steven, Gillian and Ryan.