Take a standard circular saw, run the side closest to the blade against the base and cut along all the base. It wouldn't take much with a decent pry bar to pop the chunks out. A jamb or toe kick saw would get very close to the base, not sure if it would get close enough to allow the shoe to hide the transition.
In my last house I popped the trim, layed the floor and re-installed the trim, and it didn't require a shoe. I wouldn't leave chunks of the old floor there...but that's just me.