One thing you have to keep in mind is that the katana you find in the game are not ancient medieval katana, but more likely modern reproductions for example the field katana produced for the Japanese army in world war two, and made more like a regular western sword than a katana, using tempered steel and no special/indepth techniques in a factory. Although there are still some sword-smithies operating in Japan I believe, so its possible but unlikely its a modern forged blade (They're hella expensive iirc). Although if I recall a lot of the techniques have been lost. At least they'd most likely be made of steel.
So most likely they would behave more similarly to a saber or falchion of the west than a true katana. At least in terms of cutting edge and durability.
And if they are intended to be the real deal 300 year old swords... what the hell are random drug dealers doing carrying them around or rotting in peoples basements?
Good point. I did a bit of google research - your average modern katana is about 1kg, your average falchion is between 0.5 and 1, your average broadsword is between 1 and 2kg, scimitars are about 1.5kg and a rapier is 1kg. All about the same, really.
Probably 90% of all swords you'd find these days are modern junk designed to be sold to people who think swords are 'cool', and many of those are decorative quality only. They're not actually sharpened and many would collapse after a bit of use because the handles aren't really attached well.
While a really good sword would be a godsend against zombies, you're not actually that likely to find a decent quality one unless you get really lucky. A standard hardware store machete would actually be your best bet, really, since chopping down small trees and shrubs and actual extended use is pretty much perfect for fighting zombies. Old military sabers would be good too, since those were also designed for real combat use (specifically slashing).
This game really needs quality levels for items beyond simple damage levels to reflect that, though.