”En kok” isn’t a male body part, but means ’Chef’ in Danish – as in a person that cooks. In rural areas though you may still hear people refer to the loud noises in the morning as “kokken galer”, and then it is the rooster they are referring to. Not the local chef.
A rooster is called “en hane”, which confusingly is the exact same word in Danish as a faucet… This can be avoided by referring to one located by the sink as a water faucet: “en vandhane”.
A female chicken is called “en høne” and their offspring “en kylling”. Not to be confused with a young cat, that’s “en killing”.