The Hexblade warlock's Hex Warrior feature says (emphasis mine):
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. [...] If you later gain the Pact of the Blade feature, this benefit extends to every pact weapon you conjure with that feature, no matter the weapon's type.
Does this allow me to use my Charisma with 2-handed weapons (provided it is my pact weapon and my Hex Warrior weapon)?
This question is not the same as Do the Hexblade warlock's Hex Warrior feature and the warlock's Pact of the Blade feature refer to 2 different weapons, or the same weapon?. That one is asking how many weapons; I'm asking if the term "type" means two-handed weapons, or something else (e.g. slashing or ranged weapons).