What's the risk of embolism and/or necrosis after nonsurgical nose reshaping?

What is used?: Not clear what 'nonsurgical' nose shaping you are asking about. Use of fillers (like injectible silicone to accepted materials) have potential of damaging blood vessels and causing tissue loss & bear the potential of entering into the venous system around the nose which can embolize to the cavernous sinus in the cranium. Can be life threatening.

Very minimal: If you are referring to injectable fillers i feel it should be less than 1% in capable hands. The nasal vasculature at risk for an embolus is subdermal (just under the skin) and the vast majority of filler needs are deeper tissue planes. With small amounts and careful observation, emboli causing any necrosis resulting in scarring can be avoided. Aestheticspecialtycentre.Com.

Small but real risk: Injectable fillers may be used to to minimize appearance of the nasal hump. While this can be a quick "fix" does not permanently improve the appearance of the nose and does come with certain risks. Blood flow to the skin can be disrupted with filler injections - inadvertent injection into a small blood vessel or from pressure on blood vessels or skin itself - may result in tissue death/necrosis.