I found when my kids were little that the sunhats HAD to have a velcro or tie up strap in order to stay on their heads. A good fit is also important. Nobody wants to wear a hat that keeps falling into the eyes, or on the other hand, is squeezing their little head!
My thoughts on the sunglasses: if they are wearing a proper hat (which is preferable) they don't need to wear the glasses. In fact, through personal experience, I would rather not put sunglasses on little ones.