I would rather have a semi-auto 12 gauge and a long machete as backup. Here's why:
Although you are right that a headshot is desirable, it requires that the nervous system becomes disfunctional, such as with decapitation or a splattering of most or all of the brains out the back of the head. The higher the nervous system is destroyed, the better, as if the zombie is chopped in half at the waist, it could still pull itself along with its arms, so best go for the head or neck. But remember, it might take more than one small caliber hits to the head to actually destroy its brain to the point it cannot move at all.
Stay informed, stay alive!
Don't get bit, and Happy Hunting!