In his response to the question, Dr. Hatem Al-Haj, dean of the Shari`ah Academy of America, stated,

May Allah reward you for your pious caution, and enable you to maintain it. You should indicate to the interviewers before the meeting that you don’t shake hands, and you should use body language that would convey that message. That could include carrying a brief case in your right hand. If one was forced into shaking hands by the pressure of the situation, one may thereafter ask Allah for his forgiveness, but should do his/her best to avoid it, as much as they can.
a physician may treat a member of the other gender if a same gender physician was not readily accessible to them. The burden of seeking a same gender physician is on the patient.
You may wear scrubs that go down to the knees and wear wide pants underneath them. Some conservative Christian nurses wear scrub skirts as well. I would recommend this to be the other piece underneath that scrub top that goes down to the knees.
May Allah help you!