As far as I know, you will need to go through each reservation to get the card numbers.
In theory you should only need the credit card number for specific events, like preauthorizing the card as each reservation comes in or charging for no-shows. Each of those tasks would be a one-time operation, so getting the card number from each reservation would make sense. A bulk download of all the CC numbers at once would probably violate some kind of PCI compliance regulation, or at least look suspicious. Although if you have a lot of reservations to preauthorize, it would certainly make the work go faster.
If you do find a faster way, please let us know!