Rhinoplasty and TMJ: Scared of rhino because I have bad TMJ.

In my experience improving nasal breathing can help significantly with TMJ disorder symptoms in the long run.  In fact, I work with many dentists to improve the nasal airway for just this purpose.  This improvement happens because you sleep better with less obstructions which means a less stressful sleep.  This decreases bruxism (clenching) and therefore pain in the joint.  The nasal surgery itself can trigger a short term worsening of pain due to the reduced breathing postop.  This can happen even if the nose isn't packed, because of swelling.  Cosmetic goals can be accomplished during the same surgery to improve your health.  
Of course if the surgery is cosmetic only, then surgery could be limited and the postop swelling limited.  The decision of open vs endonasal is more of a conversation of what you want to accomplish and how comfortable the surgeon is with doing those techniques.  GA vs sedation will really not affect the postop swelling.  
I would see a ENT/ facial plastic surgeon to not only evaluate the outside, but the airway as well.  IMO, patients are never happy with the appearance if they can't breathe. 
I do not believe that a non-operative rhinoplasty would accomplish your goals.  
All the best

 When performing a rhinoplasty procedure, it's important to have a controlled airway so that blood does not pool in the back of the nose and go into the trachea. In our practice, we do not perform rhinoplasty procedures under IV sedation, since osteotomies must be performed in the nasal bones to narrow them after the dorsal hump removal. TMJ should not be a problem, since we place a laryngeal mask airway in place and  patients are not fully  intubated with an ET tube. The dorsal hump removal and narrowing the  bridge line can be accomplished  with a closed rhinoplasty approach with all the incisions placed on the inside of the nose. No  painful intranasal packing is required. In our practice, we do not recommend nonsurgical rhinoplasty due to the fact that it is only temporary, is not FDA approved that application, and can have significant complications such as skin Necrosis. Rhinoplasty is a very difficult endeavor, so choose your surgeon wisely based on extensive experience producing natural results consistently. Digital computer imaging would also be helpful to understand what can be accomplished with your nose upon your facial features. This can be performed at the time of the consultation, or online. For many examples of close rhinoplasty, please see the link and the video below