Getting a large mole removed that is right underneath my nose?

I went to see a doctor about a mole that is directly below my noise. Every time I get a cold it breaks open from blowing and bleeds. The doctor that I saw said she would refer me to a plastic surgeon as there is a high possibility that if she removes it, it will raise that side of my lip. I saw another doctor that said she could just shave it for me so I wouldn't have to go through the steps of seeing a plastic surgeon. What would you say would be my best option.