Do You Need a Stylus for Call of Duty 4: Modern Warfare on Nintendo DS?

No, a stylus is not required.

Call of Duty 4: Modern Warfare on DS is controlled entirely with the physical buttons:

• D-Pad / Face Buttons: Movement, aiming, shooting, weapon switching, stance changes, interactions.
• L / R Triggers: Aim down sights / Fire (or swapped, depending on control scheme).
• Touch Screen: Used only for the map (tap to zoom), menu navigation, and occasional minigame interactions (e.g., hacking, dialing). You can navigate menus with the D-Pad and A button if you prefer.

You can play the entire campaign and multiplayer without ever touching the screen with the stylus.