What is the point?
First, what uses disk space is not the Browser, but the User Data, there is already a CommandLine Switch: --user-data-dir= to accomplish what you want, which is to start Brave and use another location for the user data.
But anyway, Brave uses the OMAHA updater, which is open source alternative to what Chrome uses, and probably what Edge uses as well.
OMAHA update can only update in two locations, Program files when you install with admin rights and %localuserdata% when you install without admin rights, but the user Data never changes, it always goes to where it goes.
Brave by not having a custom installer, they have the way to use Policies and all that which is good for enterprise, unlike other Browsers.
So, in that case, what you have to move is the User Data.
Brave in their Github page already offers a zipped version of the Browser which doesn’t have the updater, which means you can place it anywhere you want, and then you can create a BAT file or Shortcut and use whatever directory you want for the User Data.
You can use --user-data-dir="User Data" and the folder will be placed wherever the Brave.exe you are starting is.
If you want to keep the ‘updater’ but move the files, then you should use Junctions or Symbolic Links, which is exactly what Windows users all over Windows, so using them will not cause issues.
The best way to use it is by installing Brave without admin rights, so everything Application, Updater and User Data will be placed in the same folder, in %localappdata%\BraveSoftware
Then you use move it somewhere else and create the junction or symbolic link to it in the same place so Updater and everything works as expected.
It is the way Chromium works, this has to be something Chromium offers easier without using the --user-data-dir=.
Other Browsers like Vivaldi or Opera which offer custom installers, and they even offer standalone versions, they are not doing anything differently, they are using the same Commandline switch to place their user data in the folder where you ‘install’ their standalone version. They just do everything automatically, but doesn’t mean users can’t do it.