Yes, you can use two handed pact weapon with CHA modifier
Type"Type" refers to a single entry in the Weapons table such as Sickle or Maul.
Interestingly enough, the Player's handbookHandbook never refers to weapon types as it does for tools or armor. For armor PHB p144 explicitly states:
The Armor table collects the most commonly available types of armor found in the game (...)
The fact that weapon types by analogy"weapon types" are analogous to entries in the weapon table is demonstrated by the Kensei Weapons entry in XGtE p34:
Kensei Weapons. Chose two types of weapons to be your kensei weapons: one melee weapon and one ranged weapon. Each of these weapons can be any simple or martial weapon that lacks the heavy and special properties. The longbow is also a valid choice.
ThatThis means that that the benefits of the Hex Warrior feature also extend to e.g. Greatclub, Glaive or Pike that you conjure with the Pact of the Blade feature,.