Hypophora is also known as anthypophora and Sylva Rhetoricæ explains that it is
A figure of reasoning in which one asks and then immediately answers one's own questions (or raises and then settles imaginary objections). Reasoning aloud.
Anthypophora sometimes takes the form of asking the audience or one's adversary what can be said on a matter, and thus can involve both anacoenosis and apostrophe.
That site gives this example of its usage:
"But there are only three hundred of us," you object. Three hundred, yes, but men, but armed, but Spartans, but at Thermoplyae: I have never seen three hundred so numerous. — Seneca
Although hypophora and anthypophora once meant the same thing, they have drifted apart in recent times. Wikipedia notes that
A division has arisen between the definitions of hypophora and anthypophora. The Century Dictionary identifies hypophora as the dissenting statement or question and anthypophora as the reply to the question. Thus the two terms have come to embrace both elements of hypophora, as well as dealing with the whole concept.
Your question appears to be about the hypophora portion alone, and I can tell you that there appears to be no more specific term for that concept. You can get by simply by calling it a "rhetorical question," and though that is much more general a statement that is the one that will be more familiar to your audience. Unless that audience is well-versed in rhetoric, the more precise terms are likely to produce only blank stares.