Schaper in 1982 tennis pro and won the following year the Challenger tournament of Nairobi . In 1985 he won his first double title on the ATP World Tour alongside Alexander Antonitsch . Overall, he was able to win three double titles in the course of his career. He reached the individual finals of an ATP tournament four times, but was never able to win an individual title. He reached his highest ranking in the tennis world rankings in 1988 with position 25 in singles and in 1991 with position 37 in doubles.
Between 1982 and 1990 Schapers played 24 singles and 12 doubles games for the Dutch Davis Cup team . His greatest success with the team was taking part in the first round of the world group in 1990 against Germany . In the 2-3 defeat he lost his singles against Carl-Uwe Steeb as well as the doubles against Eric Jelen and Michael Stich alongside Tom Nijssen . He won his last individual against Jelen. At the 1988 Summer Olympics , he competed for the Netherlands. He advanced to the quarterfinals, in which he was defeated by the later gold medalist Miloslav Mečíř .
Even before the end of his professional career, he was coaching Daniel Vacek and Alexander Rădulescu , and from 1993 he was full-time coach of Vacek. Between 1998 and 2000 he was team principal of the Dutch Davis Cup team.