In canon, I don’t think Wookiees were used as slave labor for the first Death Star.

It goes like this:

Geonosians had the design, which they may or may not have created (at the very least they modified it).
The Republic stole the designs during the Battle of Geonosians.
A secret Republic war council authorized building it because they were convinced Count Dooku was building his own with another copy of the designs.
Orson Krennic was assigned to oversee the project (at least eventually).
Krennic knows that they need a Kyber expert to make it work and recruits Galen Erso, his old college buddy. Erso is not told of the nature of the work, just that it’s about providing more efficient energy for the Galaxy.
The Empire happens, and work continues. Geonosians are used as slave labor. They rebel and their world is sterilized in retaliation.
Erso figures out what’s really going on and escapes with his wife and daughter with the help of Saw Gererra.
Work stalls, Tarkin is assigned to oversee the project. Krennic is still in charge of the engineering aspect, Tarkin is basically his supervisor.
Rogue One happens.

I think that’s it, but it’s been a while since I read Catalyst, so I may have gotten a couple things wrong. Might check Wookieepedia later and make some corrections.