OFCCP does not have specific guidance on confidential searches. Absent that, OFCCP will look at it the same way as any other job you are required to post. You still have an obligation to post it. You may have a search firm post it for you to the local ESDS and you will need to provide proof of that posting as well as a record, such as an email exchange with the search firm and the two job descriptions, showing that this job posting is for your company’s job.
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.