I don't think you can do this with fetch. What you are looking for is a "shallow clone", which you can do from a single branch or tag in the repository. Something like
will get you just the code for that specific tag. Note that it's still ~6GB.
That's just the Chromium code, though. I have no idea how (or even if) it will work with the rest of the build infrastructure; by not running fetch, you won't have gclient set up, you might not be able to easily get the correct build dependencies or third-party libraries needed. You might try following the rest of the instructions at
https://www.chromium.org/developers/how-tos/get-the-code/, but I expect that you will probably have a difficult time getting it to build.
Ian