If you can dream it, you can do it!
Seriously though, I have seen people who have private practice come into the university setting like once or maybe even twice a week to supervise residents in Dermatology outpatient clinics.
If you want to do academics then I would consider doing a PhD along with your MD training, depending on where your interests are. It may not be needed. But if you want to focus on basic science, design new therapeutics, or even develop new skin disease diagnostics it could help. There are also MPH programs where one may focus more on Epidemiology. The sky is the limit, to be honest. In other words, create yourself and your career! 🙂
Regarding administration, sure. Go all the way and become a PD and/or chair. As far as general hospital administration, I think an general IM doctor may be better suited, and quite honestly more interested, in this sort of gig.
Dermatologists also do inpatient call in the university setting.
There's Tele-Dermatology.
There's Surgical Dermatology.
There's all sorts of options!