I have a very strange mind, which incidentally makes it that much easier to write about psycho sadistic characters in my short stories. Yes, I'm probably psycho. Seriously, no joking, I would love to see a psychiatrist just for the fun of deliberately trying to screw them around when they try to assess me.
Anyway, my point is, from that, I have a strange ability to see the weapon in anything. Leaves on the ground? Choke someone with them (also useful for anything else that can be easily stuffed down a throat). Water bottle? Freeze it and then use it as a blunt instrument. Also a handy drink when you're thirsty, if you remember to clean the bloodstains off it (or not, either way's fine ;D). Bin bag? Suffocate someone. Kitchen knives? Obvious.
So in the absence of a real weapon, which I'd probably prefer (especially since I have experience at firing a semi-automatic rifle, none whatsoever at hitting people with a frozen bottle of Coca-Cola), I could turn anything near me into a weapon easily enough.
I think when the inevitable zombie apocalypse comes, I'm going to do just fine...