You won’t even incur a bounty.
You've just escaped Helgen by the skin of your teeth, forced onto a dangerous road littered with wolves and bandits, adorned in armour pillaged from the corpses of fallen soldiers. Riverwood is friendly enough, with its inhabitants passing along supplies as you spread the word of mythical beings only thought to exist in folklore returning to life. But then you reach Whiterun, where stuffy guards refuse you entry, and even once you convince them to let you pass, pompous nobles scoff at you.
Worst of all is Nazeem, whose arrogant boasting of the Cloud District immediately made him the victim of quicksave spamming across countless Skyrim playthroughs. Decapitated, burned to death, and Fus Ro Dah'd into walls at breakneck speed — none of it was enough to make up for the insult to injury. So, modders took things into their own hands and stripped him of all his Nirnly goods.
'Nazeem's Downfall' is a mod that removes his bed (making him sleep by the well in the market), takes away all of his money, and divorces him. If you beat him up, you won't get a bounty. Mod creator Holzey suggests going as far as to download 'Bully Nazeem' so that he ragdolls as you throw punches. However, it's incompatible with 'Nazeem is a chicken literally'.
The mod also makes Nazeem shorter, but there's nothing wrong with a short king.
To make matters worse for our self-important friend, he is cursed by the Nine Divines, meaning that he has no place in the afterlife. So, when he dies, he's immediately resurrected. Combined with the fact guards don't care about his well-being, that means you can endlessly murder Nazeem in all different ways without incurring a bounty.
Holzey is also taking suggestions on how to expand Nazeem's Downfall, so if you have any ideas for how to make his life even more miserable, you can pop on over to the mod's comments section. One suggestion, made on the Reddit post embedded above, includes adding a quest where you "fight Nazeem, take his wife, take his wealth, take his house, [and put] the curse on him", letting you be the reason for his downfall.
This is a sentiment plenty of others share, arguing the downfall is too fast and that it should be slow and methodical, letting us watch him lose it all. Other modders, however, have taken a different route, turning Nazeem into the Jarl of Whiterun. Truly, there's a mod for everyone.