The Death Star was possibly Geonosian designed, and mostly built with machines, and Geonosian and Wookie labor
The Rogue One novel Catalyst has many references to this:
[more on the way]
[Krennic speaking to Geonosian Poggle the Lesser] "I'm certain you had all sort of weapons planned to pad the Separatist arsenal...What I'm most
interested in is the deep-space mobile battle station...The one I'm
referring to is the size and shape of a small moon."
Poggle at one point claims though that Count Dooku provided the basic plans and "the Geonosians had merely refined them" but later:
"Krennic smiled to himself: Poggle was finally taking credit for it."
So in this case, it is somewhat hard to pin down the exact source of the design because both Poggle and Krennic are largely unreliable.
Additionally - when Krennic inspects the work in progress:
Krennic felt that the holovid didn't do justice to the work in
progress above the planet Geonosis...
"What you see is a product of countless hours of construction work
undertaken by machines", Gubacher continued
"Geonosians would be the first to inhabit those immense life support modules...tens of thousands of drones had been transferred"
 source: Aftermath novel:
Wookiees were used across the galaxy too...in building structures like
the Death Star