Yes, driver is a private individual; a taxi driver, not a guide. We have used him for Delphi, the Peloponese, Temple of Poseidon, and transfer to ship.
For Rome I strongly recommend Scala Reale, now known as Context Rome, for walking tours. We took a number of their small group tours and one private tour.
There are lots of great train trips in Switzerland but I don't know if I would recommend as a post cruise; there are always plenty of opportunities to get to Europe. If anything, I would recommend three days in Rome followed by short flight to Paris and three days in Paris then home.