Well, a cleaver is not actually a weapon. Though it’s designed to carve through meat, it doesn’t expect the meat to be moving (or at the very least fighting back).
The cleaver is a cross between an axe and a knife. It’s top heavy, so like the axe, when you swing you commit. Unlike the axe, it doesn’t get good rotational power and you can’t change direction mid strike. Swinging a cleaver, you’re going to hit something… though it probably won’t be the thing you want. Cleavers are also meant to be used one handed with the intention that you’ll be bracing the object with your free hand.
If you feel you need to use something like a cleaver in your story then grab a machete.
I’m not sure what you mean by hooked knives? Do you mean a gut hook knife? If so, then no probably not. Again, a gut hook knife is a tool and it’s meant for use gutting a kill after it’s already dead. It’s not going to give your character any real advantage in combat over someone who is using an actual weapon.
If you mean the Chinese weapon, the hook swords, then yes. They are normally dual wielded. However, as with any weapon or martial style, be careful about taking them out of their native environment. Beyond the concerns about appropriation, it’s important to do extra research to determine who and what the weapon was used against. Many weapons lose their advantages when taken out of their social and historical context as many cultures developed their own styles of combat and faced different challenges. Also, be careful of East versus West and Orientalism. Basically, if you’re not planning on using Chinese culture and history as a base for your setting along with doing tons of research don’t go there.
Going back to the cleaver, the problem with improvised weapons is that they’re improvised. They work well in a pinch, when you’re desperate, but if your character is planning on going into combat then they probably have time to find a real weapon. A real weapon will fulfill it’s purpose best as opposed to one it’s being jury rigged for. If you use a weapon as a tool you risk damaging it so it can no longer fulfill it’s function, the same is true of a cleaver or a gut hook knife. You can use them in a fight if you really have to, but you probably would rather they be functional later after the fight is over.