You could get +15 on your Charisma-based ability scores without sacrificing too much offensive and defensive combat potency.
Our 10th level character is a Variant Human1 with the following ability scores:
- 8 Strength
- 14 Dexterity
- 12 Constitution
- 8 Intelligence
- 18 Wisdom (increased by one from race and two from ASIs)
- 16 Charisma (increased by one from race and one from Skill Expert)
They then proceed with the following classes:
- Rogue 1
- Monk 1
- Warlock (Hexblade) 1
- Ranger (Fey Wanderer) 6
- Warlock 2
1 Custom Lineage would be more flexible, but since it is less widely acceptable than Variant Human, and human does the trick, I went with that one.
You will end up with nine skill proficiencies and four skill expertises. I recommend grabbing up the Wisdom proficiencies since you have such a strong Wisdom as well. You could certainly take whatever skills you prefer, though I strongly recommend Insight as it great for a face to have.
This would give the following skill proficiencies...
- Variant Human
- Skill Expert
- Far Traveler Background
- Deception, Intimidation, Performance, Persuasion
...and the following skill expertises:
- Skill Expert
- Rogue Expertise
- Ranger Canny
This yields a +8 bonus to all Wisdom-based skills, and a +15 bonus to all Charisma-based skills.
Let's talk about your key combat metrics. The biggest thing we sacrifice by investing so heavily in to Charisma is our Constitution.
We get around our lower Dexterity by having such high Wisdom and using the Hexblade's Hex Warrior feature, but our Constitution still suffers.
Our final level in Warlock can help out a bit by giving us an infinitely renewable source of ~7 temporary hit points, but we are still fairly low on HP.
At level 10, we have a measley 69 hit points. A straight monk/ranger character not focusing on Charisma would be expected to have at least around 89 hit points; maybe 99.
That being said, the Fiendish Vigor invocation can certainly partially make up for that discrepency over the course of an adventuring day (unless it conflicts with another party member's temporary hit point engine).
Because of our substantial Wisdom investment, Unarmored Defense almost keeps up with medium armor. Half-plate grants 17 AC, while our Unarmored Defense grants 16 AC.
However, the main cost is that we cannot use a shield and benefit from Unarmored Defense. This 3 less AC is a substantial cost, and getting access to a magic item like bracers of defense would certainly be much appreciated.
That being said, 16 AC is certainly enough to be effective in melee combat. Especially considering we also get access to the shield spell thanks to being a Hexblade, and with our ranger spell slots, we can cast it a reasonable number of times per day. This more than makes up for the lack of a physical shield in my opinion.
We are pretty on par with most characters that aren't optimized for combat. Obviously, certain combat feats would be essential for getting higher damage output on a straight monk/ranger that is built for it, but as a social-encounter focused character, we hit most of the notches.
- We have Extra Attack
- We have a +7 on our weapon attack rolls, which isn't great, but is passable
- We get a free hand for the shield spell since we are using the Ranger's Dueling Fighting Style
- We can use a shortsword (1 less average damage on a hit compared to the rapier) in order to also get a bonus action attack via the Monk's Martial Arts.
- We have a number of damage dice modifiers (which Hexblade Curse gives us a higher chance of doubling with a crit) including:
- the Rogue's Sneak Attack
- the Ranger's Favored Foe (since we will be saving our spell slots for shield we don't need to concentrate on anything else)
- the Fey Wanderer's Dreadful Strikes
- We have some flat damage modifiers including:
- the Hexblade's Hexblade Curse
- the Ranger's Dueling Fighting Style
While our damage output is certainly not remarkable, it is within useful ranges thanks to the Hex Warrior letting us use our Charisma.
I made some specific selections focusing primarily on the theme and requirements. There are some alternatives that can tune the character to a different play style (if I was to play this character, I'd struggle to choose between all of these):
- Rogue 2 instead of Warlock 2
I went into Warlock 2 because it helps my survivability and gives my human Devil's Sight which I find comes in quite handy at mid-tier play. I may even pick it up earlier depending on the adventure. However, another option is to sacrifice a bit of raw survivability for mobility by getting the Rogue's Cunning Action. This would give the bonus action Disengage option which is quite useful for a lower HP character.
- Goblin instead of Variant Human
Along the same lines as the Rogue option, you could get access to this Disengage choice via the goblin race. This would even give you Darkvision as well. However, you sacrifice two skill proficiencies and a skill expertise. If you are okay with less skills and missing out on one of the social expertises, this could be a good option.
- Rogue 2 and Warlock 2 instead of Ranger 6
You could also have the best of both of the Rogue and Warlock classes for survivability, but then you are barely primarily a monk/ranger at only 60% class levels. I'd probably choose this option myself as a 6th level of ranger doesn't give that much (a bit of mobility with Roving, and some more Favored Foe damage), but it does shake up the theme a bit.
- Monk 2 instead of Ranger 6
This option is pretty much reserved for if you find a very thematic or powerful magic weapon that you want to use as a monk weapon. It sacrifices some damage with the weaker Favored Foe and lack of Sneak Attack (unless the magic weapon is Finesse). However, you get access to Dedicated Weapon to make this cool weapon work with Martial Arts. You would also get access to Ki, but this is fairly mild. Maybe the occasional Patient Defense could be useful though.
- Barbarian 1 instead of Monk 1
This is clearly a big deviation as it breaks the original prompt completely, but it lets you use a shield with Unarmored Defense. You could then invest a bit more into Constitution instead of Wisdom to improve both your AC and HP. Of course this would come at the cost of your social scores since Wisdom is factoring into them thanks to Otherworldly Glamour.
- The Tough feat instead of the Skill Expert feat
If you are willing to part with a skill proficiency and expertise, you could catch up with a 14 Constitution straight monk/ranger in HP via the Tough feat (which grants a significant 20 HP). You would also lose a modifier point in one of your ability scores, so this would weaken your other metrics, but if HP is the biggest concern this is an way to help mitigate that.
- Hill Dwarf instead of Variant Human
Along the same lines as the Tough feat, you could get at least a little more HP via the Hill Dwarf. You would lose Skill Expert, but with the variable racial ASIs from Tasha's Cauldron of Everything you could still get the Wisdom and Charisma you want. This would also give some nice bonuses like poison resistance and Darkvision.
You could also use your ASI in Charisma instead of Wisdom which would improve your damage output while decreasing your AC. This is a very hard choice to make, as both are very important to your combat effectiveness. If I ended up with a Disengage bonus action I'd probably do Charisma, while I'd stick with Wisdom if not.
I know you mentioned maximizing AC in the prompt, so I'll address that here. You could certainly invest your point buy into Dexterity instead of Constitution and get your AC up to 17, but you sacrifice 20 HP to do this, which is definitely not worth it.