Great question, I would suggest that refining just the tip will leave your nose too broad and bulky up top and would put your face out of balance, would not recommend just a tip rhinoplsty on you, the lips are very pt specific, some pt's like some incisor show, others prefer none, a good test would be botox to temporarily lengthen the lip and if you like the muscle could be released with a small procedure, good luck and search to you find surgeon you trust...
The Tip of the nose can often be addressed with a minimalistic approach. It can be slightly narrowed and enhanced through a closed or an open approach. The concern for upper lip shape must be carefully considered in this setting. occasionally the lip can be lengthened resulting in a less "gummy" smile with the use of something like botox or fillers. If these treatments are not indicated, then the lip can be lengthened with a minor procedure. You should work with a facial plastic surgeon to discuss your goals and develop a plan that will help you look and feel your best. Best Regards!
Rhinoplasty is a complex procedure which requires many steps to achieve the desired results. Simple one or two step maneuvers rarely yield the results that a patient wants or believes could have been achieved. It is always best to meet with your surgeon and discuss the details of the procedure in advance of trying to decide how to do the surgery. Lip fillers may be an easier fix to your lip problem or perhaps botox for a gummy smile
Full rhinoplasty, not tip plasty is required
The nose is a three-dimensional structure, it must look good in all 3 dimensions after Rhinoplasty surgery has been performed. Performing only a tip plasty will narrow the tip, but the remainder of the nose will be out of balance to the new tip. The dorsal hump will need to be shaved down and the bridge line narrowed and refined. For more information and many examples, please see the link and the video below