Go ahead and shake that hand. It touched the door handle and the top of that chair and desk which you also touched. So, unless you're refraining from touching anything in public or at work, holding off on the handshake isn't providing the protection you're seeking. Furthermore, to be safe, you want to keep a 30 foot buffer around you from anyone else since the virus is aerosolized not only when people cough or sneeze, but even when they breathe or speak.
So... good luck!
It's common for people to focus on a few vectors of transmission but forget about so many others. I have a friend who won't touch the pole in a bus or train for fear of germs and yet he will gladly push an elevator button pushed by a hundred other people. He'll wash his hands before eating, but then shake the hand of our server.