Hm, good question. One option would be to actually define that single language like you did in your test. If you set your URL to /, you will not notice the difference to a single language page, only all text files will have the language extensions.
This would work instead as well:
I18n::template($e->getKey(), null, $e->getData(), 'de');
Don’t know if there is a better way.
Turns out you could also set
Kirby\Toolkit\I18n::$locale = 'de';
in a template or controller where you want to call the Exception method.