Yes (with limits), if you multiclass into an Illrigger1.
You've put limits at Unearthed Arcana, but I wanted to share my experiences with a homebrew class.
One of my players was in a similar situation: his character was abandoned by his patron, and he lost all his Warlock (Old One) powers after dying to a Roper. Around that time I've come to know about the Illrigger class by Matthew Colville of MCDM fame, and decided to propose that this character change his three levels of Warlock entirely for three levels of Illrigger, his backstory justifying a vested interest of Asmodeus to bring him back to life as his servant. In the Illrigger class you can find some new fighting styles, most importantly:
While wielding a two-handed weapon, you may choose to use your Strength or Charisma modifier for the attack and damage rolls. You must use the same modifier for both rolls.
This is what I was searching for, as I didn't want to force the player to rewrite his entire character sheet, and he was (still is) strongly Charisma focused, both in combat and out of it. True, it's only for two-handed weapons, and you'll lose that sweet Eldritch Blast, but it's better than nothing. My player is level 5 right now, and has expressed his enjoyment at playing the class so far. I have some concerns with the character seldom using any of his ability scores aside from Charisma, but that was a problem with Hexblade already.
1 The Illrigger class, as presented in the free PDF available from the MCDM Productions website or on the MCDM fandom wiki, is, let's say, questionably balanced, and is not the version of the class that is currently played on the mcdm streams. It breaks a few established conventions on class building (the spell progression being the biggest offender), and the feature text is quite imprecise in places, but if you're willing to put a bit of work into it, it can become a fun option. Or you can just rip the Lies Fighting Style from it and add it to normal fighting styles available or put it into a feat. What I did is make the class a half-caster, converted the Baleful Interdict to not use spell slots, but be limited by Charisma modifier, and reworked the spells that refer to Interdict seals as a collection of Battle Master's maneuver-like actions in a new class feature, among smaller changes.