To add to the other comments, but don't book it through your Southwest account. Just book it as a guest because people who do this too often can get their accounts nuked.
I would also go tell the gate agent at OAK that you aren't boarding the flight so they aren't holding the plane and making PA announcements for you. Don't tell him/her why; you don't need to give a reason. Don't lie either. Just keep it vague.