There are no codes that require a CWI for any preparation of documentation that I am aware of. In most cases a CWI is an option for an inspector but is by no means "required". Haveing a CWI or SCWI or CAWI perform any specific task is only an indication that that person has met certain requirements as spelled out in the applicable standard .
http://files.aws.org/certification/docs/QC1-2007.pdf As already indicated, the CWI standard indicates the SCWI "shall be able to" just indicates that they must have the ability to. That does not preclude a CWI or CAWI from preparing the documents.
Similar goes for inspections etc.. (except for the CAWI is the opinion of many)
Keep in mind that an individual project may have its OWN set of specifications that add to or take exception to the specific code of construction. Also, a companies internal quality program would be a document that would more clearly define the duties and responsibilities of individuals within an organization.