Stöckli began a successful curling career at the junior level, winning a bronze medal at the World Junior Curling Championships as an alternate in 1994. In 1996, he was the Swiss skip and they won a silver medal, losing to James Dryburgh of Scotland. In 1997 Stöckli won the gold medal defeating Perttu Piilo of Finland in the final. Stöckli ended his junior career with a bronze in 1998.