Non surgical rhinoplasty is a relatively new term coined in the past decade along with the flooding of the market with new providers, products and promises!
Rhinoplasty is a surgical procedure - period!
Non surgical rhinoplasty is as silly as a non-rolling car! ;)
This is a procedure offered mostly by dermatologists or surgeons who do not fully understand the nose. Fathers of the field of nasal reshaping would never, ever have coined this term or considered it valid.
The nose is a dirty place. Lots of bacteria live there. The skin of the nose is VERY thin. It's a bad combination for infection, and such infections can cause horrible scarring and irreversible problems.
Now with that said, if a patient has had an actual rhinoplasty but post op, developed a small area of depression which would best be treated with a cartilage or fascia grafts down the line, Restylane or Juvederm may be used as a temporary fix if the depressed area bothers the patient enough. The hyaluronic acids, such as Restylane and Juvederm Ultra, are the safest for the nose.
Although Radiesse is used by the providers offering "non surgical rhinoplasty," the substance is essentially bone cement and too harsh for the nose. Radiesse is best used for very deep nasolabial folds or to plump out the cheeks and the midface because it's injected deeper and has a thicker overlying cushion of skin.
Artefill or any permanent filler should NEVER be placed into the nose - ever!
Hope this makes sense.
P.S. By the way, there are plenty of surgeons doing surgical rhinoplasty in an unsafe fashion so there is the other side of the coin as well. Be careful and do a ton of research before doing something irreversible.