Your drooping nasal drip isn’t that bad. It can be shortened with either open or closed rhinoplasty. It usually depends on the surgeons preference.
The approach used by the surgeon is a function of what he is most comfortable using and not the specific problem encountered. So go on some complimentary consultations with experts and compare recommendations after a full examination and discussion of desired results and look at photos of similar patients and become fully informed about the desired procedure Dr Corbin