Despite the general belief I think guns I actually more useful than melee in a Zombie Apocalypse.
Sure melee is silent but the offset is you need to get close and whether you have a baseball bat, sword or even a chainsaw it still comes down to a 50/50 chance you kill the zombie without it overpowering you. Lets face it the average person may not be able to swing a bat effectively or may not have the stature to use something like a knife or screwdriver without putting them in equal reach and on equal height to the Zombie and as such putting them at risk. Guns however have distance. Sure by society standards especially in Britain they're not the first choice. Give a gun to a group of ten random people probably only one will be able to get a decent marksmanship score and the rest may only get a low score and that's only considering your handguns and revolvers. It would become considerably worse with long rifles and shotguns. But at the end of the day guns are idiot proof. Anyone can figure one out, hell even my own mother whose never actually held a gun ever before in her life, at a military airshow when they had guns laid out to hold and examine, she managed to figure out a Browning Hi Power in no time at all and children nearby were quickly learning how L1A1's, L85A2's, AK-47's and even GPMG's worked.
Which proves the point. Guns are idiot proof and thus your best choice in the zombie Apocalypse if your natural strength and agility puts you at an unfair disadvantage against a zombie not limited.