As you may already know, the original Axon can't handle more than 10V because that big blue capacitor is rated at 10V. You can just replace it with a higher rated capacitor (and lower mAh), thereby letting you can use the built-in Axon regulator to do what you wanted. No extra circuit needed.
The Axon II can handle up to 20V because I corrected that "mistake". (I didn't think people would use greater than 7.2V batteries when I designed the original in 2007)
The regulator is the same on both, and can handle up to 1.5A. If it overheats, it will throttle back the current automatically.