This is just a nuance, but important nonetheless:
If you say "we" don't keep your credit card number, a customer could think that "we" includes the company processing your charge. This is just not true. Whomever the merchant account holder is, and/or Authorize.net,
does keep their credit card number on file, as proof of the transaction. This is a requirement of Visa/MC among others.
If you are using a third-party provider (like 2CO etc.) and
you don't keep their credit card number, now that
is true. So in that case, you should use the phrase, "I" don't keep your credit card number. 'Cause you don't.
Then there is no question who exactly doesn't have their #.

Bailey