Yeah this would be a must I would love to relive my years of playing Ocarina of Time and shooting Cuckoo's...........then running away from said Cuckoo's as fast as little links legs would take him.
What about ammunition, metal ball bereings would be the best like it's be suggested but there could be DIY ammo and weaker easier to find ammo. What about glass marbles those can pack quite a punch, you could also find them in a lot of diffrent shop's, they also have those really big marbles they wouldn't go as far but would cause some damage.
https://erandika.files.wordpress.com/2012/09/marbles_110.jpg
Also something I have made before would be distraction rounds. I have made sling shot ammo with wax paper, tape and a bunch of bang snap's. You open up a bunch of bang snaps and empty the contents in a square piece of wax paper, twist it into a ball then tape it shut. It's then basically a giant bang snap so you just have to hit it on a hard surface and Bang!, it actually took some bark of the tree I just threw it at as well. For gamplay you could craft it with wax paper, Tape, Firework powder(silver fulmenate) and gravel, then craft it into a ball and you can use it to distract and draw the attenion of players and zombies. It's loud and produces a bit of smoke so it would definitley get someones attenion.