Yes, but how would you ever get her to agree to it? You could get a hair surreptiously, but then she'd sue you into oblivion, wouldn't she? Or can this be done legally without the person's consent?
I'm thinking a hair could be found at a booth in a restaurant (or something similar). Do the test. If it proves a relationship, "leak the results" to the world. Someone will pick it up. Remember, it's not the nature of the evidence, but the seriousness of the charge!