It did help that Edward Lhuyd, a Welshman and a linguist, went around Cornwall taking notes of the speech back when it was still spoken, and recording it in phonetic notation—a sort of early precursor to the International Phonetic Alphabet.
So I believe some of the revived pronunciation is based on the notes that he took, and some on the English accent of West Penwith, the area where Cornish survived longest, on the theory that the Cornish spoken there may have influenced the sound of the English there and that the typical English pronunciation heard there may give us clues to traditional Cornish pronunciation.
But actual sounds recordings we do not have, as you say, so we cannot be completely sure.
And so scholars disagree on some of the finer points of pronunciation, or things such as how many distinct vowel phonemes there are, or exactly what they sound like, or whether there were three length distinctions (short, half-long, long) or just two (short and long), and so on.