If we develop military spaceships will they use Naval or Air Force rank designations?

No, I’m agreeing with it completely.

The concept of the “General Officer” in the West originates with the Captain-General, AND the rank/billet/posting/grade that in Anglophone armies is referred to as “General” with no qualifier, descends from the Colonel-General.

The job/rank titles of the USPHS, with corresponding Civil Service grades and such:

“Non-supervisory”
O-1:Junior Assistant Whatever/Ensign/GS-9
O-2:Assistant Whatever/Lietenant Junior Grade/GS-10
O-3:Senior Assistant Whatever/Lieutenant/GS-11
O-4:Full Whatever/Lietenant Commander/GS-12

“Mixed Supervisory and Non-supervisory”
O-5:Senior Whatever/Commander/GS-13,14
O-6:Whatever Director/Captain/GS 14,15

“Senior Supervisory”
O-7,8:Assistant Surgeon General/Rear Admiral(Lower Half)/SES
O-8: Deputy Surgeon General/Rear Admiral(Upper Half)/SES

These are temporary rank/grade/titles:

“Political”
O-9:Surgeon General/Vice Admiral/(Political Appointee, Temporary)
O-10:Assistant Secretary of Health Affairs or Something Like It/Admiral/(Political Appointee, Temporary)

NOAA also has a Navy style rank structure.

As for the topic at hand, the Air Force and Navy have most commonly contributed military personnel to the space program. I suspect that a “rank merge” will take place at some point in a new service…It depends on how you view the capital space ships … if you view them as big-ass carriers a la Space: Above and Beyond, you get a “Vacuum Navy.” If you view them as little air force bases that happen to move around, you get the air force structure…