Welcome.
Overall, I think you should be able to talk intelligently about more than derm-path or path - even if this is your ultimate goal. Being able to compare and contrast different shadowing experiences (and career paths) will make a stronger impression on you.
I think (hope) you are kidding, but the "delivering babies" comment would probably be a dead-giveaway that you have not spent much time in other fields.
When an adcom member asks you "why this school?"
how would you answer? (rhetorically, I am not asking you to answer)
Are you interested in private practice? tertiary care? academic medicine? solo practice?
These are the kinds of questions you will encounter along the way.
Furthermore, you need to do yourself a favor and keep an open-mind in medical school. There may be something you love you don't even know exists. As such, you really owe it to yourself to shadow a variety of doctors in a variety of settings.
Finally, "the best laid plans of mice and men..." You don't know what will happen in medical school. You really should think about making sure there are alternative careers you could be content with. Path (and derm-path) are actually not guaranteed residencies for you (or anyone). Not to be a negative Nancy: This is a huge investment of time and money. Show that you have considered multiple paths forward - even if you have your heart set on one.
Best of luck.