Since the Hexblade warlock's Hex Warrior feature changes your pact weapon's attack modifier to use Charisma instead, does it also turn booming blade's modifier from Strength to Charisma?
Hex Warrior and booming blade can work together.
When you attack with that weapon, you can use your Charisma modifier, instead of Strength or Dexterity, for the attack and damage rolls. This benefit lasts until you finish a long rest.
"That weapon" being either the daily touched weapon or the Pact of the Blade weapon. I'll call it the HW-weapon for short.
When you cast booming blade, you have to make a melee attack with a weapon. Usually, that involves using either the Strength or Dexterity modifier, because that's how the typical rules for attacks work - not because booming blade asks you to use either modifier.
If you make that melee attack with your HW-weapon, then you follow the Hex Warrior rules as you would for any attack with your HW-weapon and add your Charisma modifier instead of Strength or Dexterity.
The key point here is that Hex Warrior does not modify the booming blade cantrip; rather, it modifies the melee weapon attack made as part of the booming blade cantrip.
Booming Blade has no modifiers
Booming Blade adds thunder damage to your weapon's normal effects. Those normal effects include your Charisma modifier for your pact weapon. Booming Blade doesn't undo the Hex Warrior effect, but neither is there any modifier to apply to the Booming Blade's effect because of it.
Booming Blade is an additional and independent effect
The Hexblade warlock's Hex Warrior feature (Xanathar's Guide to Everything, p. 55) partly says:
Whenever you finish a long rest, you can touch one weapon that you are proficient with and that lacks the two-handed property. When you attack with that weapon, you can use your Charisma modifier, instead of Strength or Dexterity, for the attack and damage rolls.
The booming blade spell description (SCAG, p. 142) states
As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell’s range, otherwise the spell fails. On a hit, the target suffers the attack’s normal effects, and it becomes sheathed in booming energy until the start of your next turn. If the target willingly moves before then, it immediately takes 1d8 thunder damage, and the spell ends.
This spell’s damage increases when you reach higher levels. At 5th level, the melee attack deals an extra 1d8 thunder damage to the target, and the damage the target takes for moving increases to 2d8. Both damage rolls increase by 1d8 at 11th level and 17th level.
As a Hexblade warrior, you use Charisma as your damage mod for the attack's initial damage (whatever type that is) plus an amount of thunder damage from booming blade.
Then, if the target moves willingly, it receives an additional amount of thunder damage. You do not add your Charisma modifier to either the initial damage or movement-based damage dealt by booming blade.