You don't take a .app out of a signed archive and expect to be able to submit it, regardless if you use Transporter or not.
The whole purpose of an archive in your example is to create something that is properly configured/packaged/signed for submittal to the store. If it isn't, you can submit/upload it.
If for some reason you don't want to archive using Xcode, google the process to create an archive via the command line. But if your ducks are in alignment to be able to do that, Xcode should work as well, so...
Your issue's root cause is being space constrained. To fix that, you'll either need to free up sufficient space and keep it there, or buy a much larger drive.
As for running Xcode from an external drive - Xcode should be installed and run from your boot drive, /Applications folder, internal or external is ok, but again only if you're talking about the boot drive...way too many system hooks for it to tolerate any other configuration.
Good luck.
