That style looks really good man. I wouldn't do a strap if I were you, cause I personally think this is a good look. A balbo is a good look too, and I haven't seen many of those around, so it'll look pretty original. But do as you please, it'll always grow back. If opinions is what you wanted though, I have provided you with mine. Keep it how it is or go for a balbo. Either way, if I were you, I'd let the mustache grow. It's definitely strong enough to give a little more edginess to the look.