I have a WPF application that is capable of being used both with a mouse and using Touch. I disable all windows \"enhancements\" to just have touch events :
Something I used for an application once, was to simply setup a custom cursor whose image was simply a blank .CUR file.
As for the second problem, I would have indeed suggested moving the cursor to another location, but then I saw you'd done the same thing. If you application won't run in full screen, you can just define that safe position to be the lower-right corner of your application window.