Wünschig appeared in the singles draw of the 1979 French Open and lost his first round match to Australian player Warren Maher, in four sets.

[1] A month after the French Open he represented West Germany in a Davis Cup tie against Romania in Bucharest, one of the Europe Zone quarter-final fixtures.

His match against Dumitru Hărădău started the tie and he defeated the Romanian to give West Germany a 1–0 lead.

[2] On the Grand Prix tennis circuit he played only in home tournaments and had wins over Harald Elschenbroich, Bruce Manson, Haroon Ismail and Cliff Letcher.

In doubles he and Reinhart Probst were surprise finalists at the 1980 German Open, a Grand Prix Super Series event.