Hi,
Next version of HikaShop will have a plugin to have all the emails sent by HikaShop stored in the database, including the contact notification emails, which will contain the values of the custom contact fields.
So that would need your primary need to storing the contact form data in the database and being able to review them in your backend.
Regarding the credit card storage, I guess that a small customization of the plugin storing the contact email would allow you to cut the credit card number in two and keep half in the email that is sent and the other half in the copy that is stored in the database.
Note however that the next release is scheduled for September. If you need something before, then that would require the development of a custom plugin to store the contact data in the database.