Benny89, if someone is interested in a DPR-only focused two hander this is useful. But Soulblighter said two levels of Hexblade - that doesn't let you use two handed weapons with Hex Warrior. You'd need a third warlock level to pick up Pact of the Blade to do that. Charisma also helps other aspects of a character including saves, more skills than STR, spell DCs, etc.
If someone is looking for information on a particular build, going off on a different build isn't particularly adding to the conversation.
I do like your enthusiasm. Considering looking for a build using a non-two handed weapon (so GWM would only grant bonus action attacks on crit, no -5/+10, and PAM would limit you to suboptimal Spear and Quarterstaff) for CHR based wielding, what would be your recommendation for race? Preferably looking beyond DPR to more holistic measures of success.
Just to clarify: for Variant Human you want to use STR, not CHA because you don't have enough bonus as Half Elf and good feat that can give +1 and give something beneficial (like Elven Accuracy). So for Variant Human DPR PAM build- 1 level of Hexblade is only taken for: Curse, Shield spell, 2 cantrips, 1 short rest slot (for Bless/Hunter's Mark or Shield) and 3 other spells. We don't want CHA on PAM builds, not worth it.
Now to your question about CHA-based build:
If you want to use 1 handed weapon: Half-Elf hands down. I said that Half Elf is the best race to pick for Sword and Board Vengeance/Hex build because you don't need: PAM and GWM.
So I definitelly recommend Half-Elf here for Sword+Shield build. Half-Drow best for Fearie Fire. The build would look like that:
STR: 13 (we need that to multiclass out of Paladin), DEX: 14 (for +2 bonus to medium armors), CON: 13 (we will even that with RES (CON), INT: 8 (useless), Wisdom: 12 (+1 to WIS is always good) and CHA: 17 (we will even that with Elven Accuracy).
You can also go: 15,12,13,8,12,17 to be able to wear plate armor.
We want to start with Paladin level 1 Vengeance. We will use rapier + shield because our DEX is at +2 vs +1 STR. Next level we take 1 level of Hexblade (Pact of Blade) and we get to use our CHA for one-handed weapons. Now we will be having +3 using our CHA 17. Any one-handed weapon will work now. Then we will continiue Paladin levels till we get to level 6 Paladin (level 7 character) to get Aura as fast as possible.
Now for feats:
Level 4 Paladin (level 5 character) we will grab Elven Accuracy: this will even our CHA to 18, giving us +4 to attacks with one-haded weapons using Hexblade and already giving us later +4 to saves from Aura.
Now after level 7 we have two options: continue Paladin all the way (19 levels) to not lose ASI or take 3 more levels of Hexbalde to not lose ASI too.
Because we get all ASI only if we do either 19/1, 16/4, 12/8 etc.
In my opinion taking 2 or 3 levels of Hexblade is bad because you lose one ASI. Also for our optimized Half-Elf Vengeance - 1 level dip Hexblade gives us everything we need. If you really want to get Agonizing Blast + Darkness + Devil Sight combo I would go 16 Paladin/4 Hexblade. Then you lose high-level slots for smites but you get Agonizing Blast + Darkness Devil Sight combo if you like that.
So I recommend here after 7 level to continue Paladin till the end, then at next levels we grab:
Level 8 Paladin (9 level character): RES (CON). This gives us now 14 CON so +2, Aura gives us +4 and we are proficient in CON which at this level gives us another +4. So overall we have 2+4+4 = +10 CON saves throws which makes us automatically pass any DC 10 Concentration save.
Level 12 Paladin (13 character) we grab +2 CHA ASI.
This gives us now our full potential and best Half-Elf Vengeance/Hex optimization:
We have 20 CHA so +5 to attacks on level 13 (amazing). We have Elven Accuracy so rerolls on advantage (VoE), we have +5 Aura save throws (amazing). We also have proficiency in CON saves which at level 13 gives us: 2+5+5= +12 DC throw on Concentration, so we are auto-pass on DC up to 12 and easy pass DC 15 and even DC 18+ will be much easier.
We will use Medium Armor (because only 13 STR, unless you find STR boosting items) so our AC will be 17+2=19. For Fighting style I recommend Duelist by default or Defense for low magic campaign to even up AC to 20 (22 with Haste). But by default: Duelist.
So our Half-Elf looks like that on level 13:
STR: 13, DEX: 14, CON: 14 (Prof), INT: 8, WIS: 12 (Prof), CHA: 20 (Prof)
Feats: Elven Accuracy, RES (CON), CHA+2
Fighting Style: Duelist
Aura bonus: +5 to all saves
Concentration Check: +12 to Concentration save.
This way we can go in fight with Haste/Bless all day and not worry abou Conc Check most of the time, we have +5 to attacks with CHA, we have Curse, Elven Accuracy and 3 attacks per round with Haste at 1k8+2+1k8+5 with +5 to hit and vs VoE target= triple d20 roll on one attack. And we have free bonus action each turn so we go VoE first turn + Haste so 1 attack, next turn Curse + 3 attack (19-20 crits, Evlen Accuracy) and next turns we go full ham.
Everything looks the same if you/he decides to go 4 levels of Hexblade instead of 1 level dip, same feats etc.
With 4 levels Hexblade you get also Darkness + Devil Sight which gives us total not of THREE possible ways to get advantage:
1. Vow of Enmity
2. Fearie Fire from being Half-Drow (if allowed)
3. Darkness + Devilsight combo
This is best build you can do for Half-Elf Vengeance/Hexblade build. It's not as much nova/dpr as Vuman Pam but you have better save throws and better hit chance due to 20 CHA and Elven Accuracy. So you will hit more often for less damage.
Overall in my opinion this is second best possible build for Vengeance Paladin for damage behind Vuman PAM, but definitely this one is safer and more all-around as on level 13 you have: +1 more to hit, +2 more to save throws and better advantage tools (Fearie Fire + VoE assuming 19/1 build as I recommend). To compare Vuman PAM on level 13 have: PAM, GWM, RES (CON) and 18 STR (if he didn't get any STR item, because then you pump CHA). So he has -1 less to hit, but one more attack and +10 to damage. So overall it's a matter of difference between: better accuracy (rerolls) vs more smites and much more dmg spikes.
The other variant of this Half-Elf build is to give up +2 CHA at 13 level and grab GWM and use greatsword, but then you need 4 levels of Hexblade to not lose ASI and to be able to use GS with CHA. And our CHA 20 would be pushed back to level 17. That would make "Nova" variant of Half-Elf build.