I think instead of getting a new weapon, the old weapons should be reworked to have a niche. As it stands right now, the only weapon worth using past wave 1 is the Katana. Let's post ideas as to what we think the current weapons should do.
Knife- Keep it as is. Everyone has it, no need for anything special.
Machete- Tough call on this one. Almost nobody uses it, and it's barely an upgrade to the knife. Personally, I think the machete should be replaced with a blunt option like a sledgehammer or something. The sledgehammer would have slow attack speed like the fire axe. Primary fire could do slightly less damage than the fire axe but can daze or stun any specimens other than Fleshpounds and the Patriarch for 1 second or so. Alt fire bumps this time up to 3 seconds as well as doing slightly less damage than a fire axe alt swing.
Fire Axe- I like the ability to break through doors suggestion, but I don't really see it as being all that useful if you play with decent players (I personally host a listen server for my girlfriend, my friend, and his little brother and we all work together fairly well). I think that the fire axe should be capable of cleaving. Primary fire would do what it currently does; a moderately slow high damage swing. Alt fire, however, would swing the axe in a 120 degree arc in front of the Berserker. This ability would have a 2 second or so "reload" time since it takes a lot of effort to carve through several specimens at once. I think this would give the berserker an option for when they're surrounded, and would allow them to compete with other perks that can take out crowds of specimens from a distance.
Chainsaw- This one is a bit of a tough decision for me. I liked the chainsaw prior to this patch, but since the specimens all got health buffs the primary fire has been rendered fairly useless. I want to say just buff the damage on it so it's capable of killing a clot via decapitation again like the combat knife can do. Maybe lower the run speed nerf a tad as well, considering that husks can hit a chainsaw wielding Berserker like shooting fish in a barrel.
Katana- Don't change a thing on this one. I think that most Berserkers are comfortable with it now. If anything, increase the price to make it less attainable so early.