The mechanic? You hold the delayed dead ball just for a moment. You don't run around the field with your arm sticking out.
In the play you describe, you decide at the moment of OBS where she would have gotten to had there been no OBS. You give the signal, hold it for a second or two, and then continue to officiate. You might have this girl protected all the way home on that OBS... but you don't hold your arm up until she gets there!
