We have several boxes full of signature cards that we would like to shred if possible. Is this permissible if they are scanned into our system and viewable through an image? What is the length of time a bank must retain the actual card after it is scanned?

I don't know that there is a time requirement if you are scanning them. I think that as long as you keep them long enough to make sure that you have your image and you have your server backed up. Maybe 6 months.

As soon as we are certain the imaged card is legible and printable, we shred the signature cards, usually about one week later.

Don't forget to check your state requirements, they could be different!