I wouldn't try to do this itinerary on my own. With the guided tour you are paying for expertise, logistics management, pre-planned accommodation and meals, information from a knowledgeable tour guide, etc. Without all that you are going to be spending all of your time just trying to figure out how to get from A to B. Plus that itinerary looks too rushed for me anyway even under the best of circumstances.
Slow down. Reduce a workable itinerary. Use public transportation or cheap guided day tours from a home base. Plan to come back later.
As a general rule, I like to stay four nights in a "place". A place can be a major city (Paris, Rome, Munich, etc), a country (Belgium, Denmark, etc.) or a local region (the Loire Valley, Swiss Alps, Normandy, etc) depending on what they have to offer. From your home base you can also take day trips to nearby cities or attractions. I have found that doing a guided day tour or two is a reasonable compromise in between the long term group bus tours and trying to do everything on your own.
For a two week (16 day) trip, I would pick four "places" that are reasonably connected by train or bus. You can still rent a car at a particular location to explore the region, but most places in Europe are workable without one.