As I understand the trackball link you provided you can create macros for the mouse. That may be one way to accomplish the "flip" requirements.
However, I wondered about the "build of this mouse is angled" and took another look at the mouse photographs.
Referencing the 3rd photo down from the top. Is that what you mean by angled? So that leads me to believe that you are mounting the mouse on an already angled surface - correct? With the end objective/requirement being that the ball and switch surface is "vertical" .
My suggestion would be to just create some sort of spacer or wedge to place behind the mouse that makes everything vertical and allows normal mouse orientation. The spacer being placed between the backside/bottom of the mouse opposite the scroll wheel.
That said, how do you plan to mount the mouse to the wall in any orientation? Velcro came to mind as an option but velcro may not be real secure or lasting.
Remember that the mouse will need to be easily removable to change batteries.
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If possible, take a couple of photographs and post here via imgur (www.imgur.com
). Be careful not to include any personally identifying information in the photos.
The photos may help solicit additional ideas and suggestions.