You can fly alone but will lose the value of the campanion. You might try checking in for you wife from home that will keep the seat empty at least till the 10 minute point. If the flight is full they could still put someone in the seat when she does not board but it will be the last seat they fill since she would be checked in. Also you can check with the gate agent about leaving the seat open but that seems to create more confusion than it helps. They seem to want to open up as many seats as they can.
FYI sometimes reservations will change the name for $100.