Don't be afraid of the resulting lesion. Clean it well, remove everything that looks like waxy pus. But look for a feather follicle in the center that may be looped and growing back into the tissue. Like an ingrown hair follicle, feathers sometimes get stuck and don't emerge fully, forming...
It's not easy to judge a two dimensional photo, but it appears likely to me to be a giant feather cyst. It looks like it's just under the top layer of tissue. Does it appear translucent around the base to you?
Try moving the mass. Does it seem to "float" at the base? Or is it firmly anchored...