Penis is the formal and the scientific word. People often try to find some euphemism or evasion along the lines you mentioned. But if the circumstances demand that you use the name of the organ, penis is the word you can use without giving offence.
I recently overheard a conversation between two women, in which one advised the other to consult someone else. The indignant reply was: "Why? Because he has a penis?" Had she used any other word, she would undoubtedly have offended some people.