Using a different character controller

Basics of swapping Controller

Yes , you can - but you will need to setup the child objects in the same way as the one you see below or as the example in the demo scene:

Can I use a different Character Controller with this system?

How to disable movement?

The "AKDisableManager" script has a reference to the player character on this example:

using UnityStandardAssets.Characters.FirstPerson;

[SerializeField] private FirstPersonController player;

public void DisablePlayer(bool disable)
        {
            if (disable)
            {
                AKUIManager.instance.isInteracting = true;
                crosshair.enabled = false;
                player.enabled = false;
            }
            else
            {
                AKUIManager.instance.isInteracting = false;
                crosshair.enabled = true;
                player.enabled = true;
            }
        }

You will want to edit the reference variable and the lines below to incorporate disabling your character movement and camera rotation:

//Reference your character controller here, unless your controller solution comes
//with a better solution
[SerializeField] private FirstPersonController player;