You're wrong. Go back and read his battle against King. We can see a distinct difference between when he's using CoC and not.
The lightning around the sword tells us he's using CoC. It's the same when he first coated his swords with CoC which caused the fodder to lose consciousness.
When there's no lightning he just using CoA haki.
When there is lightning he's using CoC and CoA.
In this particular scene we see when he coated his swords with CoC to make it KoH attack.
The vivre card tells us the black lightning (flash) is CoC haki.
The lightning around the sword tells us he's using CoC. It's the same when he first coated his swords with CoC which caused the fodder to lose consciousness.

When there's no lightning he just using CoA haki.

When there is lightning he's using CoC and CoA.

In this particular scene we see when he coated his swords with CoC to make it KoH attack.

The vivre card tells us the black lightning (flash) is CoC haki.
We saw the same lightning when base Luffy kicked Kizaru that doesn't mean base Luffy used conqueror coating against Kizaru.
CoA is also black in color.
How does King panels prove it when base Luffy also had the same lighting streak against Kizaru