Sounds interesting - I'd go with very little at first to gauge the heat.
As for the ginger, I'd juice some to get maybe 1/4 cup [or add one or 2 tbs.] and add one or 2 tablespoons of cayenne? Only guessing here, but if not enough, you can always add more the next time...
Don't want to burn those aforementioned delicate parts :) !!!
That would mean the end of the experiment.
BTW: Make sure not to get into eyes [very important], or submerge head - the H2O2 (Hydrogen-Peroxid) will discolor the hair.