Automate Cash Sale After Fulfillment

My apologies if this question has already been posed elsewhere - I tried searching but only found questions relating to automating cash sales when sales orders are saved.

Is there a way to automatically create a cash sale (specifically, to bill a credit card) once an order has been fulfilled?  We've had a few instances in which an item was back-ordered for a few days (long enough for the original authorization to expire), and the payment is declined when we attempt to bill it out after it has shipped.  We're then left with trying to get a new payment method from the customer and/or intercepting the package to bring it back to us - it's a big hassle.