He started teaching choral conducting in 1952 and was appointed vice director of the department for church music in 1954.

In 1958, he was awarded a prize by German broadcaster Südwestfunk (SWF) for his composition Musik auf Christi Himmelfahrt (Music for Ascension).

[1] He published sheet music, including reconstructions of Bach's Ärgre dich, o Seele, nicht, BWV 186a for the Third Sunday in Advent,[2] Singet dem Herrn ein neues Lied, BWV 190[3] and the St Mark Passion.

He collaborated with singers such as Peter Schreier, Aldo Baldin, Ria Bollen, Ursula Buckel, Eva Csapó, Agnes Giebel, Julia Hamari, Ernst Haefliger, Philippe Huttenlocher, Georg Jelden, Helena Jungwirth, Siegfried Lorenz, Adalbert Kraus, Horst Laubenthal, Karl Markus, Barbara Martig-Tüller, Friedreich Melzer, Klaus Mertens, Siegmund Nimsgern, Ernst Gerold Schramm, Verena Schweizer, Jakob Stämpfli, Ortrun Wenkel, Kurt Widmer and Edith Wiens.

Hellmann conducted the Requiem by Jean Gilles, Haydn's Harmoniemesse, the Oratorio de Noël by Saint-Saëns,[5] Beethoven's Missa solemnis, the four Choralkantaten by Max Reger,[6] and Frank Martin's Golgotha.