Resolution:
It is not possible to disable the audit logging functionality at Trading Partner level or Operation ID level.  It is possible only at the BC engine level. You can only disable audit logging functionality for all Operations, all Trading Partners and not for individuals.

However, BC 5.3 includes a new feature, called User Management that allows Administrators to control individual user access to BC Administration functionality.  Please review Chapter 4 of the "BC Concepts Manual" for details.