Is Nostril Reduction Under Local Anesthesia Non-surgical?

Having nasal surgery under local anesthesia isn't non-surgical. A non-surgical Rhinoplasty refers to injecting the nose with a tissue filler. Its also called injectable rhinoplasty or the 5 minute nose job (although it usually takes 20 minutes!).

The term "non-surgical" is used to describe any technique that does not involve cutting (i.e., incisions). It does not refer to what degree of anesthesia is used.
So a procedure such as nostril reduction that is performed under local anesthesia (injections of numbing medicine) is still "surgical." Typical non-surgical treatments include things like Botox injections, injections of wrinkle fillers, chemical peels, etc.

Reducing the size of the nostrils can be a very difficult procedure.  If the tissues do not heal as planned irregular shapes to the nostrils or unsightly scarring can occur.  It is best to make certain that the procedure is indicated and performed by someone with experience in this technique.

There is no passing out, this is a bad thing.
You may have general anesthseia where you are carefully monitored as your consciousness is decreased and you are "put to sleep" so to speak.
Local anesthesia involves shots into the area to be operated. Frequently the surgeon can give an Rx for sedatives to ease your anxiety.
If there is cutting and sutures, it is surgery regardless of the anesthesia. All surgery and anesthesia requires care and planning to optimize safety and outcome.
sek

Nostril reduction always requires surgery, meaning cutting out some of the tissue. You can't really make it smaller if you don't take some out. Citting means surgery. Surgery can be performed under different levels of anesthesia: local only, local with some sedation, or general. If you have it under local anesthesia only with no sedation, there might be some pain or discomfort during injection of the anesthetic itself. You can discuss it with your surgeon.

 Nostril reduction or alar base excisions can be performed under local anesthesia. The injection will probably be uncomfortable, but after the initial injection it is rather painless.