Hi, Andrew. Your approach on rewiring is exactly right. With the layout as you describe, it should be a relatively simple job to rewire without tearing up your walls. Some electricians are very good (or very lucky) with the fishing tape used to pull wiring through walls. But each house is different and no one can give even a rough estimate without seeing it. Likewise, it is a good idea to upgrade your service to 200 amps.
As far as doing some of the work yourself, you can certainly discuss this when you call at least 3 electricians for a bid. They will be able to more accurately discuss your capability to do the job and their willingness to supervise your work. By the way, when you go out for bids, you will find that they normally spread into 3 categories; there will be a contractor or several with low bids and they might not do good work or will substitute lower quality parts than you want, there will be some at the high end and they are so busy that they don't want the work or want to use higher priced materials than you need, so your best choice is usually the one you like best from the group in the middle. But check their bids closely to se if they have allowed for you doing some of the work yourself or other issues.