Would an alar base reduction suffice? (Photo)

A rhinoplasty specialist will be able to comprehensively address the issues you have with your nose.
Alar base modification is an effective way to reduce the flare and/or width of the nostrils. Showing us a base view (photo from bottom up looking up into your nostrils) is the best view to evaluate your nostrils. Excess width can be reduced with sill incisions, excess flare with Weir incisions, and excess flare + width addressed with a combined Weir+sill incision.
Consult with 2-3 of these surgeons in person and determine your comfort level with their approach, demeanor, and before and after results. Good luck @asianrhinoplasty

It's not exactly clear form the photos whether your alar base is particularly wide.  The appropriate width should be the same as the distance between the inner corners of your eyes.  With that being said, you may actually benefit from a rhinoplasty in which the tip can be refined with slight increase in projection and derotation of the tip.  This can be achieved utilizing your native cartilage (either septum/ear/rib depending on the amount needed) so that you can avoid any foreign objects in your body.  Also by raising the tip, this will give your nose a narrower appearance and even without changing your alar width, as it will transform your nasal tip from a trapezoid to a triangular shape.  

In my opinion an alar base reduction performed carefully as a wedge would flatten the alar flare. This can be performed without excising any part of the nostril sil which can narrow the nostril airway ( i.e the inlet for the air ). In my opinion only proceed with what you feel unhappy about. Performing a full on rhinoplasty augmentation with grafts is a major undertaking and if you do not want this do not be persuaded to do so.There are some videos on my Instagram account @mrjagchana which you can find by scrolling down.