You have posted nice side-view photos of your profile and goal, but frontal views are missing, as is physical examination of your nose! You are already asking if your proposed surgical solution can be achieved, and thus far, 5 of my colleagues are eager to agree!
But not so fast!
Is your bump bony or cartilage, or a combination of the two? The latter is most likely, and simple rasping does not work well for cartilage. Since your hump reduction requires true finesse and accuracy, trimming of the cartilage requires a blade, not a rhinoplasty rasp (or "file"), and doing this precisely can be difficult from a closed rhinoplasty approach. Since there is less ability to precisely control hemostasis from a closed rhinoplasty approach, scar formation may replace the tiny amount of hump removal achieved. And, if indeed you have a wide bridge or develop an open-roof deformity after even modest hump removal, osteotomies and infracture will be necessary to prevent a truly "fat-nose" look from the front. More potential bleeding, scar fibrosis, and/or uncertainty of result! Now we have a fine kettle of fish, don't we!
Another discussion item that has thus far been neglected (but would likely not be during in-person evaluations), is determining just why you feel your nose looks "fat from the side" when your actually cute and diminutive nose would look substantially more small (or at least harmonious with the rest of your face) if you have a small anatomic chin implant for your retrusive chin (in addition to or instead of hump removal)!
Please see several ABPS-certified plastic surgeons who are experienced in rhinoplasty and offer comprehensive evaluations of your facial aesthetics. The above topics should be explored in detail, the pros and cons of the various issues being considered, and what works best in each specific surgeon's hands. Seeing before and after results is also helpful, especially since your requests are not for dramatic changes, and every operation has small changes that are uncontrollable, such as bruising, swelling, scar formation, etc. If your nose was a block of wood, then simply "filing off" the bump a tiny bit via the most inconspicuous approach would indeed be a good plan. But the nose is living, bleeding anatomy comprised of many types of tissue, each responding differently to surgical manipulation. Keep that in mind as you hear each surgeon's recommendations! Best wishes and Happy New Year!