Let's answer this question slowly: Do black swan cygnets typically know both of their genetic parents?
Up to one-quarter of monogamous black swan pairs are same-sex, with males taking over a female's nest to raise her young without her. One-third of monogamous black swan pairs show extra-pair paternity, with the male aiding the female in raising another male's offspring. A cygnet is a juvenile swan. So the answer is no.