If my son's father isn't on the birth certificate does he still have to sign over his rights for someone to adopt him?

I'm trying to join the air force and I have to sign over my rights to my dad. My son's father was never a part of his life and he now resides in prison on a 60 yr sentence for child murder from his ex. He always denied he was the father. Could I also just state that I don't know who the father is? Would they let my dad adopt him then if that was the case?