An option not yet discussed but touched on by @LizzzyJo is to cut the thing off at the skin level and let it be.
This is an option sometimes chosen by first responders to accident victims that have been impaled by a wooden stake or arrow shaft. It relieves the pain of having the thing leveraged...
I would first determine if it's a bone or a feather. Snip and inch off the end and look at it. If it's hollow, it's a feather shaft. You can safely yank it out of his neck if it is.
If it's solid, it's probably a bone. If you look at the center with a magnifying lens, and you see pores, it's a...