Trooper, you're right. It's not a generic Close Combat Weapon, it's a Plague Knife. Plague Knives are listed in their wargear; it's not a special rule that modifies their CCW, it's actually a different weapon. I just spotted this recently when Army Builder wouldn't let me swap the knife, and then checked the wording in the codex.
So you have to trade your bolter or bolt pistol for a power fist, power axe, etc. Probably best to drop the pistol if you're taking a fist, or drop the bolter if you're taking a power weapon so you don't lose an attack in assault.