I use a slingshot to chase the cats out of the garden when they want to stare at my little furry darlings at the nut bar. The cats hardly come anymore, have had enough of me probably peppering their fails and backs. I absolutely like cats and usually do them no harm, but if they go after my squirrels I know no pardon. At those 18-20m shooting distance from 5 meters high, I am infallible with my slingshot.
An apocalyptic zombie is much bigger than a squirrel, he would have no chance.
Real strong slingshots with stabilizers are banned in Germany.