Shaw was born in St. Thomas, Ontario. He played his junior hockey with the Kitchener Rangers of the OHL from 1981-1984. In his rookie season with the Rangers in 1981-82, Shaw earned 31 points in 68 games. He added four points in 15 playoff games as Kitchener advanced to the 1982 Memorial Cup. In five games in the tournament, Shaw had two assists as Kitchener won the Memorial Cup. He would be drafted by the Quebec Nordiques as the 13th overall pick in the 1982 NHL Entry Draft.