Do your hands shake just from nervousness rather than from any medication or lack thereof?

Try holding something in your hands at all times. I always hold a pen... it looks natural, as if I am "ready to take notes" and you can figit with it a little bit without it calling attention. I just switch it from hand to hand if I have to shake hands with someone for instance.

It helps a huge amount.

You can also hold something that feels nice to touch. I keep a smooth stone in my pocket that I can grab and just hold if I feel nervous or figity, it takes my mind off the nervousness.

But the reason the pen is nice is that no one will question why you are holding it.

Best of luck on the job and congratulations!