chanter, cantor, (πρωτοψάλτης) precentor, according to Stavropoulos. But is the dictionary explaining the Greek term, or giving an equivalent which could be used in an English text? And if so, what kind of text?
The Bank of English has 70 citations for chanter and chanters, of which 32 occur as proper names or in titles. The next most frequent sense is the pipe of the bagpipes which plays the tune (about 16 citations), then follow others including people shouting slogans, and people whose function it is in certain societies or religions to produce chants or sing.
Besides these, an internet search on psaltis on http://www.google.com produces examples from orthodox church texts in English, where the term is clearly regarded as a technical term and is simply transliterated, along with other terms like kontakion (see for example http://sf.goarch.org/Voice/Winter2001/Cappella.htm). But this is a technical text, in the sense that its topic is orthodox music and it is addressed to people who already know something of it.
The present text is a general interview. How much knowledge can you assume of your readership? How much explanation could you put in without making Theodorakis sound like a schoolteacher? Would an expression like "were you in the church choir?" help the readership? Would it distort the Greek?
cantor and precentor are much more restricted than ψάλτης, being more highly technical and not words to be found in everyday conversation.
τροπάρι hymn, chant (but chant could lead to problems of interpretation, since the main sense today is rhythmic shouting of slogans)
ψέλνω sing, (εκκλ) chant, according to Stavropoulos. The collocation in English however is sing hymns. The difference between sing and chant is not so much whether this activity takes place in church or not, but whether the words are written as verse (which hymns in the western churches are) or not (e.g. psalms and responses in the western churches, for which chant is a more likely verb). chant by itself does not imply a religious text; in English one can chant slogans.