Create a fsm on your "screen gameObject" with Mouse Enter Event in one state and connect it to another state. In that second state use Set Cursor action.
Then add Mouse exit event to return to first state for example.
later..
To avoid using raycast for distance measures, could add a isTrigger Collider, so when Player enters the trigger zone, that "screen" fsm starts to react.
Hope this makes sence:)