As explained by Varg Vikernes in his books, the word “elf” derives from the PIE root *albho- and it means simply “white”. This matches with the fact that the elves represented the spirits of the dead. It makes sense because the dead were buried with white clothes, their dead bodies became quickly very pale and they were purified by death (white is the colour of purity/purification).
In my opinion swans are an avatar/manifestation of the elves and thus of the ancestors. The word “swan” derives from the proto-germanic *swanaz (“singer”), in the meaning of “singer bird”, and from the PIE root *swen- (“to sing, to make sounds”).
Swans are white, as the elves; they live in the water (which symbolizes the amniotic fluid), regenerator element…waters in the European mythologies are at times indicated as portals or passages for the realm of the dead/burial mound. Finally, swans are believed to “sing” before their death and we know that the elves traditionally like to sing, recite poetry, poems and tell stories. They do it as often as they could. Elves and swans sing because they are the ancestors: they try to keep alive their memory in the ancestry, keep alive the remembrance of their glory, wisdom and honour, of their deeds and achievements,
to become eternal ideals for their descendants and in this way conquer immortality. To later be chosen by a young of the ancestry and be reborn in him.
Note: The youngs that goes through the initiation ritual are also the spirits of the dead. At Yule the spirits of the dead were returning amongst the living and their families welcomed them, i.e. the dead were reborn in those children that came out from the burial mound and returned to their homes the day of Yule/Winter Solstice. The honourable dead were once again alive!
Sing, swan! Death awaits you! Memory and rebirth!