Peter did not know the woman's name. He was not insulting her by calling her "woman." If people would think he was insulting her, you could use a culturally acceptable way for a man to address a woman he does not know, or you could leave out the word.
Peter did not know the man's name. He was not insulting him by calling him "Man." If people would think he was insulting him, you could use a culturally acceptable way for a man to address a man he does not know, or you could leave out the word.