Tumors can come in all shapes, sizes, textures... I've seen dry ones, lumpy ones, ones that have burst through the skin, and ones that abcess and end up being scratched up... all on mice that is (skin cancer research).
Eggs will be safe though, you can't get cancer from eating it.
Just as a note, birds don't get drainable puss like mammals. It's a hard cheesy like stuff.
I personally would not take a chicken to a vet, but my chickens are not of pet status.
Quote:
This is my first thought also.
If it is not an oil gland tumor/abcess, I am one who would probably remove the thing by cutting/pulling it off even if it does bleed and then letting the hole heal.