Best Rhinoplasty Procedure to Fix Wide Nostrils?

The computer-imaging you provide seems to be a realistic expectation after Rhinoplasty Surgery. You see narrowing of your nostrils and tip, along with correction of your tip asymmetry that is causing your lower nose to drift to your left.
Your nostrils are not terribly wide, and I do not like to place any scars in the "natural seam of the nose" (nice description). Although these external scars may heal well, they may be unsightly and require subsequent dermabrasion. I like to keep the nostril-narrowing scar well concealed in the base of your nose (nasal sill).
I hope this is helpful for you.

The type of alar base reduction your surgeon is describing is quite appropriate for narrowing the nostrils and when done with meticulous technique, the scars should be a non-issue.
I caution patients, however, that narrowing the nostrils can make the tip of the nose look wide or at least out of proportion. It's important to adjust not just the nasal base, but also a corresponding amount of nasal tip and bridge to achieve a pleasing appearance. Computer imaging pre-op can demonstrate this effect and help patients (and surgeons!) visualize the intended result.
Keep in mind, though, that spreading of the nose when smiling is normal and is not really correctable with rhinoplasty (at least not if a natural appearance is desired).
All the best,
--DCP