Can Tip Reduction Be Performed Under Local Anesthesia?

Yes it can be done. But based on your posted photos you need to allow the rhinoplasty surgeon you used to do a complete corrected operation. If you are directing the operation by first having a rasping than now wanting a tip plasty. YOU NEED a combination under local/sedation at best. 

Revision rhinoplasty for the wide nose with asymmetrical tip can be done to give a better looking nose. You should see an experienced revision rhinoplasty surgeon who does natural noses.

While local anesthetic may seem easy, it limits the surgeon with regards to what can easily be addressed. For example, if cartilage needs to be harvested from the septum, the procedure becomes more involved than a local will allow. The best option is to find an experienced rhinoplasty surgeon and discuss in depth what he/she is most comfortable with- sedation may be an option for you. Some tip narrowing may be advantageous, but your bony width also must be factored in- if you are not going to have your bones broken/narrowed your tip must not seem overly narrow for the upper nose. Also, it appears that you have a weak chin- have you considered a chin implant? With a soft chin, the nose appears larger. Balancing proportions and features is the artistic part of rhinoplasty- and the reason experience is so crucial. Good luck!