"Beat 'em or burn 'em; they go up pretty easy."
Clubbed muskets and bayonets...
Recall that the origins of the zombi arose during the age of muzzle-loading, black powder arms on that third of the "Isla Española/ Hispaniola" occupied by French slave plantations, "St.-Domingue" now Haiti. Slaves labored in ways injurious and oppressive to body, mind, and social relationships, subject to life under the lash in a squalid barracks or hut. For them, nothing was more terrifying than the idea that the slave master might control one's mind and body, even after death.
Fast forward, and one has the constantly evolving, ever more novel "zombie film" or "zombie genre" combined with the last-man-on-earth nightmare fantasy. Cold War-era anticommunism led to hits like the sci-fi "Invasion of the Body Snatchers" and so on. I've watched the "Walking Dead" franchise until they killed off my favorite characters and the show--predictably--descended into another iteration of the pornography of violence. The problem all along is that everything is so utterly stock serious and grim... How the actors keep a straight face is a wonder! There is no "gallows humor" or black humor to enliven the show, and so it becomes ever more ridiculous and silly as it self-possessedly-if-absurdly plods on. The best of the genre dispense with the idea that the zombies are living dead... So, for example, I rather like "28 Days" because it is some sort of hideous biological weapon that turns people into hyper-violent asocial fiends bent on murder and mayhem, combined with the irony and yes, black humor, of animal rights activists/ "eco-terrorists" attempting to "liberate" infected test primates that unleashes it...
It might be interesting to contemplate what sorts of projectile weapons would be available for people to make or manufacture in an emergency or reversion to pre-technological eras or limited manufacturing base. Underhammers are über-simple, but of course rely on caps. Crossbows? Catapults? Bows and arrows? Pellet bows and stone bows? Plumbatae and atlatl darts? Matchlocks? Snap locks? Flint locks?
As for zombies, the all-purpose zombie disposal mechanism would have to be the Medieval Flemish goedendag or one or another feudal-era Japanese polearm.