Firearms are great, until you run out of bullets.
A disaster like this is going to throw us back in the dark ages. That means our weapons need to be a bit more rudimentary as well. A ranged weapon is safest, but still requires ammunition. The best choice for ranged defense would either be a bow or crossbow. Lucky for you, those weapons are still used in modern hunting, so they can be scavenged, along with arrows. There's one less thing you have to make yourself.
What if the zombies get close? A bow doesn't really work in melee range, so you should be prepared for that situation as well. Going with the dark age theme, a sword would be perfect, but how many people use swords anymore? A long blade tool like a machete though, now that could really fill its place.
Does this mean you should forgo scavenging and keeping firearms? Absolutely not! While they may be loud
and attract unwanted guests, they are still our best personal weapon we could have. Due to limited ammunition,
they should be used sparingly. Whether human nature is inherently good or evil, it will be inevitable
that some other survivors may find you, and want to take your stuff. There's no law anymore, so nothing
is going to stop them. A bow can be a little menacing, but a shotgun can scare people off a lot easier.
Just remember, when it comes to zombies, aim for the head.