“It was Satan who gave us shame.”
Ummmm...no. Where did you get that?
It was Satan who talked Eve into doing something shameful, and Eve who talked Adam into it.
They felt shame before God because they had acted wrongly.
Shame is a natural response to self-awareness of sin.
They were not ashamed of their bodies until they encountered Satan. And sin. Their bodies were not shameful. It was disobeying God that was shameful. When God made man and woman, he saw it as good. Not bodies to be ashamed of.