Considering alar batten grafts revision rhinoplasty. Can this be done under local anesthesia?

I had closed primary rhinoplasty and open revision with septoplasty (tip was sutured too tight, removed the suture and placed cartridge in between the domes). I am still not a 100% happy with my tip. I have alar crease shading, and it looks just a bit too narrow. I would like to get batten grafts. _ Can this be done under local anesthesia? Do Batten Grafts stay in place long term. _ What is the benefit vs risk in case of a third procedure on my nose involving only batten grafts?