Wregget played for three seasons with the
Lethbridge Broncos of the
Western Hockey League (WHL) and won the
WHL Top Goaltender Award in 1984. In 1983, he joined the
St. Catharines Saints, the
American Hockey League affiliate of the
Toronto Maple Leafs, after the Maple Leafs selected him in the third round of the
1982 NHL entry draft, 45th overall. He split time for two seasons between St. Catharines and the Maple Leafs.
Toronto Maple Leafs He made his NHL debut during the 1983-84 season while still playing junior with the Lethbridge Hurricanes suiting up for three games for the Maple Leafs. He turned a lot of heads during his first game in the league posting a jaw-dropping 48-save performance against the
Hartford Whalers to record his first NHL victory. He then split time the next two seasons between St. Catharines and the Maple Leafs. In 1984–85 he played 23 games for the Leafs while
Tim Bernhardt handled the bulk of the work. He then got into 30 games the next year as part of a three-netminder carousel that also featured Bernhardt and veteran
Don Edwards. The 1986–87 season was his first full year in the NHL with Wregget taking over the starting duties for the Maple Leafs with another youngster,
Allan Bester, completing the tandem. The following year the Leafs used the same pair for the bulk of the work with Wregget appearing in 56 games for the second consecutive season. In 1988–89, Bester, like he had the year before, posted better numbers than him, and the Maple Leafs decided to go with Bester. Wregget was traded to the
Philadelphia Flyers in exchange for a pair of first round draft picks in the
1989 NHL entry draft, and he joined incumbent
Ron Hextall in the Philadelphia crease.
Philadelphia Flyers During Wregget's first full year with the team, starting goaltender Ron Hextall battled a series of injuries and was limited to just eight games, pushing Wregget into carrying the load. Wregget played 51 games for Philadelphia before resuming the back up role the following season when Hextall returned to health. In 1991–92, with youngster
Dominic Roussel impressing during an extended look from the Flyers, Wregget was shipped to the cross-state rival
Pittsburgh Penguins as part of a blockbuster transaction, along with
Kjell Samuelsson and
Rick Tocchet in exchange for
Mark Recchi. ==Personal life==