Hmm, any tips on how I could have done it better?
By not posting it at all?

Hmm, any tips on how I could have done it better?
Well, the thinking is supposed to be that the police arrive and he changes his story, says I hit him and since I've drank the whisky and he hasn't, I'll get done for it. The joke assumes you will make that jump to a conclusion though, because he refuses the drink and you're forced to think why.
He pulls out a bottle of whisky - it's not a cheap blend - and opens it, and passes it to me. I take a bit swig of it, with a huge grin on my face, the adrenalin is leaving and I'm starting to feel good because I survived. I pass the bottle back to him, but he just screws the cap on. I ask him if he's not going to have a drink, and he says "Nah, I'll wait until after the police have been"
snip
To kill the punch line
They can prove you have had a drink after the accident.
The Halk, OT but no they couldn't (more like wouldn't) find a name for it.
The people who have a subsection for every kind of depravity said
"who cares it's ****ing ugly"
So no name.