Schüchter studied piano at the Hochschule für Musik Köln, composition with Philipp Jarnach, and orchestral conducting with Hermann Abendroth. His debut was at the Landestheater Coburg Mascagni's Cavalleria rusticana and Leoncavallo's Pagliacci.
In 1940 he was at the Mainfranken Theater Würzburg, a year later he worked at the Stadttheater Aachen under Herbert von Karajan. In 1943 he was first Kapellmeister of the Theater am Nollendorfplatz in Berlin. From 1945 to 1957 he was second conductor under Hans Schmidt-Isserstedt of the Sinfonieorchester von Radio Hamburg, in 1956 named NDR Sinfonieorchester. From 1953 to 1955 he was also principal conductor of the Nordwestdeutsche Philharmonie in Herford. Since 1959 he conducted the NHK Symphony Orchestra. His last position was in 1962 Generalmusikdirektor of the Dortmunder Philharmoniker, since 1966 also Intendant of the Dortmund Opera. He improved the quality of the orchestra and opened the new opera house with a performance of Der Rosenkavalier of Strauss, with Elisabeth Grümmer as Marschallin, Teresa Żylis-Gara as Octavian and Kurt Böhme as Ochs. In 1967 he conducted the premiere of the opera Eli of Walter Steffens after the drama of Nelly Sachs, a commission of the city of Dortmund.
Schüchter recorded operas and excerpts of operas (Querschnitte) for EMI, typically sung in German by notable soloists such as Elisabeth Grümmer and Erika Köth. In 1951 he recorded Wagner's Der fliegende Holländer with Hans Hotter in the title role, Kurt Böhme as Daland, Helene Werth as Senta, Bernd Aldenhoff as Erik, Res Fischer as Mary and Helmut Krebs as Steuermann, with North German Radio Symphony Orchestra and Choir. In 1953 he recorded, again with Chor und Sinfonieorchester des Norddeutschen Rundfunks, Wagner's Lohengrin with Rudolf Schock in the title role, Gottlob Frick as Heinrich, Maud Cunitz as Elsa, Josef Metternich as Telramund, Margarete Klose as Ortrud. In 1953 he conducted Puccini's Tosca, sung in German by Carla Martinis in the title role, Schock as Cavaradossi, and Josef Metternich as Scarpia. In 1955 he recorded Smetana's opera The Bartered Bride with the Nordwestdeutsche Philharmonie, the chorus of the Landestheater Hannover, Erna Berger, Schock, Frick, Hanns-Heinz Nissen, Christa Ludwig, Theodor Schlott and Marga Höffgen. In 1955 he also recorded Der Rosenkavalier with the Berlin Philharmonic, Leonie Rysanek as Marschallin, Elisabeth Grümmer as Octavian, Erika Köth as Sophie, Gustav Neidlinger as Ochs, Sieglinde Wagner as Annina and Josef Traxel as the singer.
In the 1960s he recorded excerpts of operas, Flotow's Martha, Lortzing's Undine (with Lisa Otto) and Der Wildschütz, and Weber's Oberon with Jess Thomas as Hüon and Ingrid Bjoner as Rezia. With the Deutsche Oper Berlin he recorded excerpts of Gounod's Margarete (with Hilde Güden), Mascagni's Deutsche Oper Berlin with Rysanek, Schock and Metternich, and Nicolai's Die lustigen Weiber von Windsor with Köth, Frick and Dietrich Fischer-Dieskau.
- Rudolf Schroeder: Das Philharmonische Orchester der Stadt Dortmund. Zwölf Jahre Wilhelm Schüchter 1962–1974. Ein Beitrag zur Geschichte des städtischen Musiklebens. Rabe, Dortmund 1982.
- Fred K. Prieberg: Handbuch Deutsche Musiker 1933–1945. Kiel 2004, S. 6342 (CD-ROM-Lexikon).
- "Gründungsgeschichte" (in German). Nordwestdeutsche Philharmonie. 2010. Retrieved 29 July 2010.
- "Vom Provisorium zum modernen Theater" (in German). Theater Dortmund. 2010. Retrieved 2 August 2010.
- "Celebrating 100 Years of Theatre Dortmund". Theater Dortmund. 2004. Retrieved 2 August 2010.
- "Walter Steffens Werke / Works" (in German). Walter Steffens. 2010. Retrieved 2 August 2010.
- "Handel Concertos Op. 7, Nos 4 & 2". Gramophone. 1954. Retrieved 4 August 2010.
- "Wagner: Der fliegende Holländer". operatoday.com. 2006. Retrieved 4 August 2010.
- "Lohengrin - Hamburg 1953 - Wilhelm Schüchter". wagnerportal.de. Retrieved 31 July 2010.
- "The Bartered Bride by Bedrich Smetana performed in German". operadis-opera-discography.org. Retrieved 22 July 2010.
- "Der Rosenkavalier by Richard Strauss performed in German". operadis-opera-discography.org. Retrieved 4 August 2010.
- Pluta, Ekkehard (2008). "Ensemblekultur". operadis-opera-discography.org. Retrieved 4 August 2010.
- "Opernquerschnitte auf CD" (in German). Deutsche Oper Berlin. 2010. Retrieved 4 August 2010.
- Schüchter, Wilhelm (1911–1974), Dirigent bmlo bayerisches musiker lexikon online, 2011 (German)
- Wilhelm Schüchter operatic discography
- Entries for Wilhelm Schüchter on WorldCat