My view on this is that "confidential preferences" are the same thing as discrimination. Sounds like this executive needs some training. However, since you are probably not in a position to suggest this, the best tact may be to find the most highly qualified candidates of all races, colors, both male and female, and if the most qualified candidate is not a white female, tell the executive this, and suggest (tactfullly) that sex and racial preference are not legal bases on which to make an employment decision (depending on th executive, the wording to this would be tricky). Hopefully, her "preference" will be swayed by the individual's actual qualifications. If not, you have a pretty serious problem on your hands, and I would take it to the next level.
Of course it's discrimination. Once those words left her mouth, she placed a rather large and awkward monkey on your back. You have obligations and one of your primary ones is to protect the assets of your company. The ONLY way to do that in this instance is to deal with it head on. By the way, you'll establish credibility in so doing. If not, you don't need to be there anyway. Look at this as an opportunity, not a position between a rock and a hard place. I don't 'feel for you', I envy the opportunity you have before you!
Does the company have any sort of diversity goals or managerial expectations for diverse population of departments?
I'd make it a point to include as broad a cross section of applicant diversity as I could possibly arrange. In addition, I'd be sure this manager had a full and clear understanding of employment law as relates to this subject plus a refresher on company policy (if there is one).