according to book 40 of conon’s 50 narrations, andromeda wasn’t sacrificed to cetus. she had a suitor named phoinix who kidnapped her, while she went to worship aphrodite. her father, cepheus, played a sinister role in the story as he secretly planned the kidnapping. perseus does save her in the end and she leaves with him, going to argos.
"The 40th story tells the history of Andromeda quite differently from the myth of the Greeks. Two brothers were born, Kepheus and Phineas, and the kingdom of Kepheus is what is later renamed Phoenicia but at the time was called Ioppa [Joppa], taking its name from Ioppe [Joppe] the seaside city. And the borders of his realm ran from our sea [the Mediterranean] up to the Arabs who live on the Red Sea. Kepheus has a very fair daughter Andromeda, and Phoinix woos her and so does Phineas the brother of Kepheus. Kepheus decides after much calculation on both sides to give her to Phoinix but, by having the suitor kidnap her, conceal that it was intentional. Andromeda was snatched from a desert islet where she was accustomed to go and sacrifice to Aphrodite. When Phoinix kidnapped her in a ship (which was called Ketos [sea monster], whether by chance or because it had a likeness to the animal), Andromeda began screaming, assuming she was being kidnapped without her father's knowledge, and called for help with groans. Perseus the son of Danae by some daimonic chance was sailing by, and at first sight of the girl, was overcome by pity and love. He destroyed the ship Sea Monster and killed those aboard, who were only surprised, not actually turned to stone. And for the Greeks this became the sea monster of the myth and the people turned to stone by the Gorgon's head. So he makes Andromeda his wife and she sails with Perseus to Greece and they live in Argos where he becomes king."
[ book 40, conon, fifty narrations, surviving as one-paragraph summaries in the bibliotheca of photius, patriarch of constantinople, written in c.63bce to c.17ce, translated by brady kiesling. ]