I still believe the ships were crewed by Cirdan's folk for both departures and arrivals, simply through scales of economy. I mean, really, how many fancy swan-prowed, grey Elvish ships are you going to make over a few millenia, several thousand? Talk about
de-elvestation of the forests. And then there is the actual act of sailing, not an easy thing in an oceanic sea like Belegaer (not many 3rd Age Elves were sailors, were they?). Finally, there is a precedent for ships arriving in the Grey Havens, as the Istari and Glorfindel both took ship from Valinor and were greeted by Cirdan. Someone had to taxi them there, and it doesn't seem plausible that Elves long resigned to living in Valinor or Tol Erressea would be enamored of leaving Aman for the vagaries of the open sea and the wilds of Middle-earth just to drop off a few dusty old men.
