Badger brush, tastefully-scented shaving cream and safety razor. Just because we're touring is no excuse to be uncivilised!
The blades for a safety razor are dirt cheap, meaning you can use them only once. Reusing a mach3 (or similar toy) will only open your skin to nasty infections while on tour.
For keeping your hair and bear in trim use a USB chargable clippers (no need for a separate power brick).