The weapon creates a wound.
I mean that even if it's a dagger used against a paladin in plate, the narrative is still about the dagger drawing blood or sinking into flesh. Hit points seem to be a bit more nebulous than that. They're a pool of points used to describe fatigue, bruising, cuts, poisoning, burns, infection, psychic pain, and so on. As such, we need to tailor our narrative to each strike. Let's consider a paladin with full hit points taking a few different hits.
From a lizardman's spiked shield: "The shield crashes into you, each spike delivering a painful bruise."
From a rogue's poisoned dagger: "The dagger thuds against your armour, and slides across to find the space between the plates, nicking your skin."
From an orc's sword: "The orc's sword comes down in an overhead arc. You lift your heavy shield high to block it and stagger back from the effort required to hold back the brute."
From a monk's flurry of blows: "The monk moves faster than your armour allows. Strikes land and miss, but all of them force you back and forth under the weight of your armour. It's exhausting."
The challenge is to find a fit between all the aspects that hit points represent and the details of the attack. The other challenge is to break the mental model that all attacks create wounds. As players we need to change the way we think about hit points.
I'll take a leaf from Vincent Baker's theorising about games. He described it as an interaction between Dice and Clouds. It's probably more accessible than using semiotics theory to describe it, so let's go with it.
The dice (the physical game component) have produced a number. The number is interpreted by the rules as a hit. The hit needs to be translated by the players into the cloud of the narrative. We know the first two parts of this chain quite well and have the opportunity to do better with the third part. Broadening our understanding of what hit points represents opens the possibilities for how to convert the interpreted die result into fiction.
So think broadly! What else does a successful hit look like in your game?