I was wondering whether in the following scenario:
Harry: Then what did you tell him?
Larry: Nothing. I just kept quiet looking at his eyes. When he found out that he had made such that big mistake and he was at fault himself while he had put all the blame on me, he hung his head in shame and walked away.
we can substitute the bold phrase with *hung his head with embarrassment without any change in meaning. Also, I need to know whether the phrase "hand one's head with embarrassment" is an idiomatic phrasing or it sounds like a weird idiom to you.
Please kindly enlighten me.