A child's t-ball bat or short softball bat would be suitable alternative since it would be easy to swing with one hand. I'd also have a machete and/or camping axe with me as well. Like another has said, sometimes, you will need a blade to clear brush or chop down limbs.
Only thing is I probably wouldn't want to use the same blade for chopping up zombies that I would to chop up an animal to feed myself or others.
So a small bat, Machete, camping axe, and maybe one of those "multi-purpose" tools with the knife/can opener/etc. as a last resort weapon and survival tool.