Devs really opened a can of worms with the 0-slot 1-handers. Where do you draw the line? Personally, I'd separate 1-handers into two groups; those with 'top-tier' stats and those with sub-top-tier stats. The top tiers would be 1-slot, the rest 0-slot. For instance, Italian Falchion is balanced with the top-tier axes, so it's top tier and should be 1-slot.
Spiked Mace, Sword, Fighting Pick, One Handed War Axe, etc are all clearly inferior than more expensive options in their respective categories, so they should be 0-slot. Same goes in 2h: Practice Longsword and the 3 cheapest 2h axes have inferior stats and should be 1-slot. Same thing in Polearm; the weakest forks, voulge, and maybe a few others should be 1-slot.
Then the totally crappy weapons (including the old 0-slot weapons like hammer/hatchet/dagger/etc) should get a "sidearm" slot of their own, so people can carry one for pure vanity purposes, or use a 1-slot bow with 3 stacks of arrows or whatnot.