If your nose truly does not need anything other than tip reshaping, then yes, the cost of rhinoplasty is usually reduced (at least in my practice). Keep in mind that there are many factors that go into the total cost of the procedure: the surgeon fee, the cost of anesthesia, facility fees, and geographic location to name a few.
Recovery is typically a little faster in tip-only rhinoplasty in that the potential for bruising and black eyes is reduced if no osteotomies are done (bony cuts performed for a variety of reasons). That being said, the nasal tip skin stays swollen longer than anywhere else on the nose. After two weeks it is typically not noticeable to others around you, but you and your surgeon will still notice. Overall swelling reduces very quickly but the last bit of swelling takes almost a year to fully go away. You will be presentable far before then however.
Based on your picture, it is difficult to know if the tip is the only area that would benefit from surgery. Often times, modification of one part of the nose, necessitates modification of other parts of the nose in order to maintain natural relationships. The best thing for you to do is to have a face-to-face consultation with one or more surgeons who specialize in rhinoplasty. And by specialize, I mean those who perform high volumes of rhinoplasty yearly (>100). If a surgeon's website buries rhinoplasty low in their list of procedures, then it is unlikely that he/she is a specialist in this field. No matter how "minor" the change, rhinoplasty is one of the most difficult and complex operations for perform well. I hope that helps. Have a nice day!