He also played for the Great Britain national ice hockey team which won the gold medal at the 1936 Winter Olympics.

Wyman, as defensive defenceman, recorded a personal best of two goals and three assists during the season with Harringay and Percy Nicklin, Great Britain's Coach, described him as having "an accurate and formidable body check as good as any Canadian".

Wyman continued to make fewer appearances before he finally retired from ice hockey in 1950 playing with Sussex in the Southern League.

Wyman was first selected to play for the Great Britain national team for the 1935 World Championships held in Davos, Switzerland.

Wyman played twice more for Great Britain at the 1938 and 1938 World Championships, winning a silver medal at the 1938 tournament and taking his total number of appearances for the team to twenty.