Predator in Call of Duty (Wii)? Not a Playable Character.

The Predator (Yautja) is not a playable character in any Call of Duty game on Wii (or any platform).

Predator Appearances in CoD

• Call of Duty: Ghosts (2013) — "Predator" DLC Pack: Cosmetic only. Predator Operator Skin (for multiplayer character), Predator-themed Weapon Camo, Calling Card, Emblem, Background. You play as a human soldier wearing the skin. Not on Wii (Ghosts on Wii U only, no DLC).
• Call of Duty: Mobile (2019) — "Predator" Bundle: Again, Operator Skin + Blueprint + Cosmetics. Mobile only.
• Warzone / Modern Warfare II/III (2022+): Predator Operator Skins (Jungle Hunter, City Hunter, Feral) in Store/Battle Pass. Cosmetic.

Wii Call of Duty Titles

• CoD 3 (2006) — Launch title. No Predator.
• Modern Warfare (2007) — "Reflex Edition" — Port of MW1. No Predator.
• World at War (2008) — No Predator.
• Modern Warfare 2 (2009) — No Predator.
• Black Ops (2010) — No Predator.
• Modern Warfare 3 (2011) — No Predator.
• Black Ops II (2012) — Last CoD on Wii. No Predator.

Wii CoD games are ports of previous-gen (PS3/360) titles with reduced features. No DLC support. No crossover characters.

If you want to play as Predator: Predator: Hunting Grounds (PS4/PC) (Asymmetrical multiplayer), Mortal Kombat X / 11 (DLC), Ghost Recon Wildlands (Mission), or CoD Ghosts/Mobile/Warzone (Skin only).