Büchel spent his early career in Liechtenstein with FC Ruggell and USV Eschen/Mauren, as well as Swiss club FC Widnau. He signed a contract with Bournemouth in August 2012. He signed a one-month loan deal with Dorchester Town in February 2013 and made three league appearances for the club. In December 2013 he joined Poole Town on loan until 18 January 2014, before moving on loan to Havant & Waterlooville in February 2014. He was released by Bournemouth at the end of the 2014–15 season, and joined Oxford United in September 2015. Büchel joined Barnet on an emergency loan in March 2017 and was released by Oxford in May 2017, after the end of the season. He then signed with Swiss Super League team FC Vaduz