My nose looks too wide and disproportionate. Is it because I have too much cartilage, and if so, can it be removed? (Photo)

Based on my research, the surgeon will alter the bone and cartilage in the nose according to what better fits the face and the needs of the patient. I understand that the thickness of the skin cannot be altered. When I smile with my teeth or laugh, my nose appears very large. I usually hold my nose in to make it look smaller. I want my nose to be less wide, my nostrils not to protrude, and overall smaller w/o me holding it in. Will cartilage be removed?