The reason most car hire companies want your credit card details is to make sure they can recover any uninsured damage/parking/speeding fines etc� incurred during the hire. A prepay card will not necessarily allow them to recover any monies (especially if its balance is zero), and so may not be acceptable to them.
I suggest you contact the hire company and explain the situation. I have heard of hire companies accepting a close relative�s credit card (who was not present at the car collection, by prior arrangement), when the hirer did not hold a credit card.