Moving between two cameras

I'm making a game in which the player controls two different characters (each one has its own empty object with a camera as child), and switchs one or another by pressing the control key. The thing is, I'm trying to make a little transition between both characters cameras by using another camera, so it doesn't just "pops" between one and another but I can't seem to do it. I tried with lerp but I don't know if I got it right, so I read and tried Vector3.MoveTowards. This is my code so far (the while is because a last-moment-braindead I had):

public class CameraController : MonoBehaviour { public Camera cam1; public Camera cam2; public Camera movingCamera;

 public bool isCurrentPlayer;

 public Transform target1;
 public Transform target2;

 public float speed = 0.2f;

 void FixedUpdate()
 {
     float step = speed * Time.deltaTime;

     if (Input.GetButtonDown("Control"))
     {
         if (isCurrentPlayer)
         {
             movingCamera.enabled = true;
             cam2.enabled = false;

             while (transform.position != target1.position)
             {
                 transform.position = Vector3.MoveTowards(transform.position, target1.position, step);
             }
             if (transform.position == target1.transform.position)
             {
                 movingCamera.enabled = false;
                 cam1.enabled = true;
             }
             isCurrentPlayer = false;
         }
         else if (!isCurrentPlayer)
         {
             movingCamera.enabled = true;
             cam1.enabled = false;

             while (transform.position != target2.position)
             {
                 transform.position = Vector3.MoveTowards(transform.position, target2.position, step);
             }
             if (transform.position == target2.transform.position)
             {
                 movingCamera.enabled = false;
                 cam2.enabled = true;
             }
             isCurrentPlayer = true;

         }
     }
 }

}