You can override the local rigidbody by using the new keyword in a local variable for rigidbody within the start function, or have it check for null within that fixed update loop. You can also just call Vector2.up.
You might run into some issues with the paddles jumping around, let us know what it behaves likes, as directly setting the velocity per frame can be testy, especially for what your looking for.
public class PaddleController : MonoBehaviour
{
public float speed;
new Rigidbody2D rigidbody;
void Start()
{
rigidbody = GetComponent<Rigidbody2D>();
}
void FixedUpdate()
{
if(!rigidbody)
rigidbody = GetComponent<Rigidbody2D>();
float v = Input.GetAxisRaw("Vertical");
rigidbody.velocity = Vector2.up * v * speed;
}
}