For many patients with thick skin, the skin is thinned out in the surgery as the tip is worked on. This really adds a lot to help with definition . Excess skin length just shrinks away as the swelling decreases. Also, many patients with thick skin actually do better with rhinoplasties because the flaps that are elevated are so firm that you can do a lot more with the cartilages and it is better hidden. Very thin skin, shows every little imperfection.
Going on several consults and getting a second, third and even more opinions is a good idea in any case. Searching for surgeons is a serious matter and you should be as comfortable as you can be with a surgeon, his skill, and his bedside manner.