I'm no expert, but when I was a kid I had an American Indian lore book that described washing feathers very gently in a wide tub (a lot like a cat litter box) filled with moderatly warm water and Ivory flakes (do they still make them??).

They would wash them gently, rinse them, and then leave them on a towel to dry. Then they'd "brush" with fingertips them to bring the featherlets (word?) back into alignment.

Again, this is just a 30+ year recollection from a book that I LOVED to read. Hopefully there are more experienced folks out there though.