Yes, you could wear the sunglasses when running. However, if you are in the early morning, I don't suggest you to wear the sunglasses when running because the sunshine in the morning is not that strong and wearing sunglasses may hinder the bright light for you. If you run in the afternoon or other time when the sunshine is strong, you could wear the sunglasses to protect the eyes from the uv.
Of course, you can wear sunglasses when you run. If you run in sun, wearing sunglasses not only make you look cool, but also shield your eyes. You know, the sun brings UV rays that can contribute to cataracts. So, It is good to wear sunglasses to shield the eyes. Besides, there are also particles and flying insects in the air, wearing sunglasses when you run can protect your eyes well. So, just shield your eyes by a pair of sunglasses.
Well, I quite understand your feelings, but as far as I can see, a lot of people wear sunglasses while running or doing some other sports. It is not a problem at all. On the contrary, by wearing sunglasses, you can better protect your eyes from some harmful sun lights. Of course it is cool and handsome. Actually, you should not care about others' opinions, just do what you think is right.
Of course, you can wear sunglasses when you are running. As we know that nowadays, there are many people who like fashion will wear sunglasses when they have activities. By wearing them, it can make them look cool and have attractive image to others. But on the other hand, you should know that sunglasses can also be beneficial to your eyes too. For example, there are many sunglasses which are designed to protect your eyes from the UV rays and the strong sunshine, for they are UV protected. So when you wear them outside to have running, you do not need to worry about the damage coming from light. Anyway, you can wear them.