Alternate payee, wife, wants to omit social security number from the QDRO and disclose it via a separate document. Her concern is identity theft. Her statement is that the QDRO is a public document. (I'm not sure how the supporting disclosure of her SSN via the other document would not be public unless it's sealed????)

OK to do this and what would be the required procedure to make sure this requirement of the QDRO is met?

The SSN is not a required element under 414(q). Therefore, a plan could approve an order that did not contain the SSN so long as the AP provided that information directly to the Plan (for example, in a cover letter to the Plan or on a W-4P).

I would accept the W-4 since it is signed under penalty of perjury

A fiduciary should be very concerned about insisting that the SSN be in the order. As noted above, the SSN is not required for qualification, and the fiduciary could have liability for adverse consequences of insisting.

By the way, domestic relations orders generally are public documents and several states and courts have adopted rules to avoid revealing SSNs in those documents.

I agree. Unless the court document is sealed, putting the SSN in the QDRO makes it available to the public. A separate letter to the plan administrator would not be a public document. Plan Administrators should have stopped requesting SSNs in the QDRO a long time ago. Now many courts are adopting rules to address this issue. How to verify the SSN is an interesting question. I'm not sure what the proper form is, though it may be a W-9?