Best way to translate parts of an existing site and retain page aliases
I have found the solution and it's quite easy actually. Here are the steps necessary:


Go to languages settings: admin/config/regional/language
Edit the default language (the one that shouldn't have language prefix).
Remove the code from "Path prefix language code" field.
Go to detection options (admin/config/regional/language/configure) and select "URL" method.


That's it, it should work as I have described in the question.