You needed an ID to cash a check for a non-customer.
That was my gut reaction. How did this transaction even get approved without and ID? This former customer's decision to not have any picture ID does not override BSA requirements. I would have told my teller to refuse to cash the check unless proper ID was presented.
Also, at what point does the CTR get completed? It should be completed by the teller/branch employee at the time of the transaction - which ensures that all the information needed from the customer is obtained.
I would be looking at your BSA policy and CTR procedures immediately to close any loopholes.
Unfortunately, I don't see an easy fix for your problem though - unless you can call this person and get a number of his picture ID from him. But since you say he doesn't have picture ID, that won't help you with anything.
The transaction did happen and you have to file the CTR. In the field I would put in "no picture ID provided; non-customer". Just be prepared to be dinged for this by your regulators and internal auditors.