It is really a difficult question to answer. Since I don't know your gender, your face or your hair style, it is hard to give you any suggestion. Sunglasses with strap are suitable for athletes or people who need to do sports in daily life. For example, we usually see many people wearing sunglasses with strap while they are riding a bicycle. For me, I would like to let my hair down to make my face look smaller. It seems no other good way to look better with it. If you don't have any sports, then you' d better to wear a more fashionable glasses to make your look better.
You could just put the strap around the head. Then you could put on the sunglasses and adjust the right position based on the position of the nose to make you feel comfortable. In order to look good, you could also put the sunglasses on the top of the head. You could do this to show your fashionable style.