What would you be using ethnicity for? I don't think they're making a case for some sort of trans-racial ethnic self-identification being used in science as a replacement for race.

I think you substitute race with precision. If a cluster of different genes or characteristics are commonly found together, say which ones you're talking about, how often they're found together (as opposed to apart), and why you think that's relevant. Talking about race is honestly often ultimately handwaving in the vague direction of 19th century biblical scholars.