I think it's logical, as you said, that they'd swear only after they heard it. If I were making a film, I'd probably use the oath you posted here (or similar) and then the Sons will just step in and in a soldier-like way say: "This we swear!" Or something like that

(in which way, Fëanor would probably first end his speech in words: "So I swear" and they'd echo it)