Can a Non-Surgical Nose Job Reshape a Button Nose?

Yes, to some degree, a non-surgical rhinoplasty can achieve minor and temporary improvement in a button nose. See Video below for some examples.

A non-surgical nosejob or rhinoplasty is when injectable fillers are used to build up certain areas of the nose, most commonly the upper bridge of the nose to smooth out a small hump in the nose. It is not for narrowing or reshaping parts of the nose, such as the button nose you describe. A button nose is due to the cartilages that make up the tip of the nose being too wide. That can only be narrowed by actual tip rhinoplasty surgery.