There is a feature available in the "New Document" form that allows a data entry user to assign saved documents to another user to just print.

If enabled, a user can designate another user as assigned printer.

Only the assigned user will see the documents, other than the originator.

In Print Assigned Documents where it differs from printing from "Print a Saved Document", any users who has managerial rights can print the saved check (the assigned user does not need any managerial rights.