If Narsil is Aegnor's sword, then we need both to get it into his hands, and to get it then to Eressea.
If Finrod receives it from the Dwarves and gives it to Aegnor, that raises the question of what his own sword is. Does he decide to give Aegnor a sword that's better than his own? Or does he have an equally awesome blade? Does Aegnor get it directly from the Dwarves instead?
After the Dagor Bragollach, Aegnor's sword (if it's Narsil) would be brought to Nargothrond. After the fall of Nargothrond, if Narsil is either Aegnor or Finrod's sword, it must be brought to Doriath, preferrably in the hands of a surviving captain (who would be the only high-rank survivor, besides Celebrimbor). I think it should not be captured by the Feanorians at Doriath, but should be taken to the Havens. There, it is passed to Gil-galad who lives with Cirdan on the Isle of Balar. Gil-galad already has a sword (and prefers his spear Aeglos) so he doesn't keep Narsil permanently, but it was his great-uncle's and so he is a fitting recipient. Having it pass through Gil-galad's hands sets up a nice parallel for when he fights alongside Elendil.
When the War of Wrath is over, Gil-galad opts to keep his own sword and spear, and give Narsil to Finarfin as a memorial of his son. But Finarfin doesn't regard a sword as a fitting memorial for a son whom he prefers to remember living at peace in Valinor before the Rebellion. So he gives it to the Eresseans, probably to Angrod after he returns to life (if we're assuming that Finrod's foreboding is correct and Aegnor himself refuses reincarnation). From Eressea it's given to a Lord of Andunie, possibly specifically so it can be used again against the Enemy when Sauron arises again.
(Which brings up the point that when we get to the story of Numenor, if we want we can give cameos to Elves who died, but came back to life, and then visit Numenor. Finrod is absolutely going to want to visit several times, and surely Turgon will want to meet Elros if he can, and Angrod and Fingon probably will want to visit, too, since they were all allies and friends with the Edain.)