I can't help you with the cork soles, but I've softened up more than a few pairs of boots, including some Army-issue combat boots that I purchased used. They were form-fit to someone else's feet, and had to be reshaped.
Essentially, I filled the boots with very hot (not boiling) water and went for a long walk, several miles, until the leather was pretty much dried out. This is an exaggerated speeding-up of the usual sweating-in process, and the leather forms very nicely to your feet. It works for cowboy boots, work boots, etc. You may want to consider whether you want to subject cork soles to this method, but unless they're weakly stitched, it shouldn't present a problem.
This is my first posting, by the way. I'm a brand-newbie. Love this site!