It's a very Romantic notion.
"Swan song" has become a metaphorical phrase in English for a final gesture, effort, or performance given just before death or retirement.
That ancient belief about the Mute Swan singing that final song is now known to be incorrect, but it was well known in Greece by the 3rd century BC. It has lived on in many references of Western poetry and art.
Actually, Mute Swans are not quite mute because they hiss. But, they do not sing as they die.
The earliest known reference to the idea of that final swan song is in Aeschylus' Agamemnon from 458 BC. In the play, Clytemnestra compares the dead Cassandra to a swan who has "sung her last final lament".
Plato's Phaedo records Socrates saying that, although swans sing in early life, they do not do so as beautifully as before they die.
In 77 AD, Pliny the Elder refuted the swan song idea in Natural History stating: "observation shows that the story that the dying swan sings is false." Nevertheless, by the third century BC the belief had become an established proverb.
The English phrase "swan song" or "swan-song" dates to the 19th century, and entered the language from the German Schwanen(ge)sang and Schwanenlied.
Aesop's fable of "The Swan Mistaken for a Goose" alludes to it: "The swan, who had been caught by mistake instead of the goose, began to sing as a prelude to its own demise. His voice was recognized and the song saved his life."
Ovid mentions it in "The Story of Picus and Canens": "There, she poured out her words of grief, tearfully, in faint tones, in harmony with sadness, just as the swan sings once, in dying, its own funeral song."
An online search for swan song titles shows quite a list of books, plays, movies etc. that keep the idea alive.
So, feel free and clear to use it metaphorically - as in "The much anticipated Apple TV may turn out to be Steve Jobs' swan song" - and also give those people at that cocktail party the truth about Cygnus olor.