Ok, so I thought of some new weapons that might fit your brief, so I’m just gonna throw them out there.
First up, the Chu-Ko-Nu:
Though deceptively simple looking, this was basically China’s automatic rifle, except for the fact that their use traces back to at least the 4th Century B.C.
Right?!
Anyway, the Chu-Ko-Nu (We’ll just go ahead and use ‘Repeating Crossbow’ from here for brevity’s sake) was a fairly simple device that allowed the user to string the bow, load the bolt and fire it all with one hand movement. You would grab the lever and move it up and down and the bow would just keep firing, as fresh bolts dropped down after each pull of the lever.
So basically a hand-cranked automatic crossbow capable of firing something close to ten bolts in as many seconds.
Interestingly their last use in wartime was in the Sino-Japanese wars of 1894-1895, make of that what you will.
Another honourable mention in this category is the Nest of Bees, China’s mounted machine-gun:

Seen here debating whether or not to destroy everything you love.
This was a hexagonal wooden box filled with hexagonal tubes, and in each tube sat a rocket-propelled arrow. This thing could launch up to 32 arrows instantly, with more power and range than a human archer could manage. Chinese armies would fire thousands of these weapons at once, basically turning their enemies into a thin red smear.
Next up we return to India, the foremost inventors of unusual yet bad-ass ways of inflicting pain on people.
I present the Urumi:

Ok, so maybe the picture isn’t all that impressive, but I can assure you that the weapon is. This is an honest-to-god whip-sword made of a flexible edged steel that is so flexible that commonly wielders wrap the blade around themselves when not in use.
This weapon is incredibly difficult to master, to the point that martial arts that incorporate this weapon always make a point of teaching it’s use last, letting students master every other form of weapon before letting them touch one.
The Urumi works much like a steep whip, in that you don’t require a great deal of strength to effectively utilise it, balance and centrifugal force do most of the work for you. Your main job as the wielder is to calculate where the blade is going, to maximise your opponent’s injuries while minimising your own.
They wanted a whip-sword? There’s your whip-sword.
Moving on, how about we go for some more home-grown savagery? I present the unnamed weapon wielded by a Roman Scissor:
These armoured gauntlets were used by a specific type of Roman Gladiator that was referred to as a Scissor (Meaning Cutter, Cleaver or Render). We don’t actually know all that much about the sport or the style, but we can infer some things from the weapon itself. The weapon allowed a wielder to protect his entire forearm, meaning that he could deflect or parry more naturally than with a bladed weapon. The semi-circular blade was made in such a way that even minuscule glancing blows would be dangerous, bleeding profusely.
It’s also a weapon that is very useful for close-quarters combat, or combat that takes place in enclosed spaces, as the length is short enough that the wielder still has a good range of movement even when the walls are close.
There was likely a proper handle on the inside giving the wielder more control and the ability to alter the rotation of the weapon.
Staying in Italy but skipping forward a bit, I’d like to introduce you to one of the weirder weapons of the Renaissance, the Lantern Shield:
“What am I?! Am I a shield? Am I a Sea-Anemone?! An abomination like me should not live!”
The Lantern Shield was at it’s core a buckler shield with a built in harness for carrying a lantern, which would shine light out of the holes in the surface of the shield. The idea was to blind opponents at night or at the dawn, and it was basically a weapon for duels. Many like the example above were customised with extra blades, spikes and gauntlets to give their wielder +2 to needless ornamentation.
While of course firearms had by this point started to render the buckler useless, duelling was still a popular pursuit among the perpetually offended of the Upper Crust, so there was a great deal of technological advancement amongst these outdated weapons.
Ooh, Ooh! I forgot about the Fire-Lance:
“Make fun of my head-snakes, will you? SHAZAM!”
This was basically the world’s first gunpowder weapon, and contrary to what you might think, it was originally a melee weapon. The Fire-Lance was a regular spear tipped with a tube filled with gunpowder and sand, and was originally used to blind or frighten opponents in close-quarters. Eventually the Chinese figured out that you could fit shrapnel, poison darts and other terrible things in there so that the shot could be a killing blow.
These weapons eventually discarded the spear part altogether, opting to use the Fire-Lance as a cheap and easy weapon for peasants and local troops to effect killing blows without much strength or training. Garrisons would keep dozens of them sitting on racks, and when under attack troops would grab one and fire it directly into an enemy’s face or chest, discarding the remains of the weapon and grabbing a fresh one.
As first attempts at something go, the Chinese didn’t piss around when it came to turning black powder into a weapon.