I'm half black and white and black guys approach me all the time. I don't have a problem with men approaching me as long as he is nor creepy. But just because a guy approaches me does not mean I will automatically like him I have to find him attractive first
Here's the thing... it's not up to you to make the call that the white man is "ugly" and dark skin man "handsome" because that's up to her and you have no idea what she views as ugly or handsome. Also there are other factors like personality which does play a huge part in who someone chooses to date. But to answer the question: no I would not freak out.