You're not Michael Jackson. I'm sure dark skin suits you just fine.
Are you afraid that people are judging you when you run outside? Of course they are. If that's too much of an issue for you, don't bother with it. But if you really want to confront your fears (and run outside in the beautiful weather), then this is something that you're going to have to do. Will you be afraid? Very, in all likelihood. But what's so bad about being afraid? Maybe you think that there is something wrong with you for being afraid. This is just not true. Perhaps it's not normal, but it's not wrong. Fear is nothing to be afraid of, it's just something that happens to people. It's just another form of pain. Do you let pain stop you from exercising? Only if it's debilitating. The pain of fear is the same. Unless it is enough to make you unable to run, go for it in spite of the pain.