Future AFROTC cadet here. I wanted to major in aerospace engineering since I was in 8th grade, but my dream school did not offer it. I have talked to several aviation/aerospace professionals at job shadows, EAA AirVenture (largest aviation gathering in the world), and online inquiries, and the only case where they would not hire a mechanical engineer for an aerospace engineer position is if aerodynamics was the principal concern of the role, in which case the aerospace engineer would generally need a MS or PhD. Most aerodynamic tasks are executed via computational fluid dynamics anyways. I bring up the private sector not because this is your ultimate goal, but instead it's where I could procure the most information on this issue.
Besides, in the AF, a 62E (if you are considering developmental engineering as your AFSC) is more concerned with project management than design/testing in most cases. Those responsibilities are usually contracted out, negating any specificity in majors. I would also recommend looking at the flowcharts for each major. I'm not sure how engineering programs are structured at USAFA, but mechanical and aero engineering are usually extremely similar up until the final year, and that discrepancy in fluid dynamics/aerodynamics/astrodynamics courses can be remedied with technical electives.
Other posters, please point out any misconceptions I may have made. Hope this helped!