Getting rhino and septoplasty done with local anesthesia & only minimal IV sedation. Can I get breathing tube to protect airway still?

Do not need one. Probably will not need an endotracheal tube for this operation. Talk to your surgeon if hou have specific concerns.
No. If you're going to have an airway - either lma or et tube - then you'll need a deeper level of sedation and the services of a crna or md anesthesiologist. Ask your surgeon about this option.
Hard to suppress. Gag reflex without sufficient anesthesia or sedation. Proper monitoring and airway protection from nasal bleeding during even sedation cases requires a crna or md anesthesiologist (if the "surgeon" is planning on doing the sedation him/herself this is not a good idea) so the cost is the same as a great and completely comfortable and safe general anesthetic. Check surgeon's credentials!

Related Questions

Can I have a endotracheal tube inserted while completely awake for nose job to protect airway if I want? Getting nose job done under local anesthesia

Maybe, maybe not. Since the procedure might break or knock out permanent teeth if you moved at all, I don't know if any anesthesia professional that would sign on for such a task. You just place your self at additional risk. If you don't trust the people doing the procedure find some new docs.
Endotracheal tube. Endotracheal tube cannot be inserted when you're fully awake because you would not be able to tolerate anything down your airways without coughing and laryngospasm (spasm of your voicebox). Only when the muscles are paralyzed by anesthetic or when you are out of it due to a respiratory distress you can have endotracheal tube placed.
See below. Most "awake" endotracheal tubes are placed under sedation for the patient in special circumstances where the airway must be secured with the patient "awake". It is an uncomfortable proposition that I would suggest avoiding. Local anesthesia with sedation for nose job is usually sufficient for the case. Discuss your concerns with your surgeon.
Rhinoplasty. You will not be able to tolerate an endotracheal tube without sedation.