Can I Reduce Nose Wings Lenght Only with Cartilage Removal? (photo)

My nose tip is very round and my nostrils are visibly assymetric. I was wondering if it's possible to make it look like the after pic I did on photoshop without having to cut it open from outside and reposition it. Like, would it be possible to make it shorter removing cartilage through a closed rhinoplasty? And at the same refine the tip like it shows on the pic and still look natural? Would you say I'm a good rhinoplasty candidate or is my nose good as it is? Thank you.