How to smooth drooping buccinator muscles right under corners of my lips? (Photo)

From your photo, it appears that instead of  drooping buccinator muscles, you have herniation of the buccal fat pads. These are very common and can give you an unwanted fullness in that area. Removal of the buccal fat pad herniation is done under local anesthesia either intra-orally or laterally combined with a SMAS facelift. At 41 yrs of age, an intraoral approach would probably be the best option. A thorough examination with your surgeon will give you all of your options.
John Standefer MD

A combination approach would give the most improvement. I recommend fillers for the lines themselves but also lifting around the mouth and cheeks to build underlying anatomical support. In our practice we combine sculptra with other fillers "layered" on top and lasers, rf treatments, J Plasma and peels to get the most conservative natural look. Please see a facial sculpting expert. Best, Dr. Emer

Looks like you may have buccal fat pad herniation as another surgeon here has pointed out. Removal of the buccal fat pad can be done under local anesthesia or sedation. If instead you are worried about hollows, you may want to consider fat grafting as a more permanent solution. Hard to really tell from the single photo. Examination in the office would help the plastic surgeon ascertain what the cause of your cosmetic concern is and properly advise on which techniques are best in your case. Like some other practices, we also use surgical simulation software in our office to help patients see possible results of surgical maneuvers on a 3D model of their own faces. This is VERY helpful in educating patients.