If you enter your room reservation number and the system works properly, then you will be able to give just a credit card hold for the CRT reservation.
If the system does not work properly, it will not recognize that you are on the dining plan, and you will either have to pay in full to book online or make that particular reservation by phone.
You will always have to give a credit card number for this reservation, either for a reservation guarantee or to pay in full. If you object to providing your credit card number online, then call and make the reservation. If your objection is to giving a credit card number at all, then there is no way for you to make this reservation.