We had a similar situation. Initially, we used the Additional Language of the website (a special version of the language for in-context only). This language was omitted in the language selection tool on the website, and we added an extra placeholder to the website URL (instead of “website .com” we created "website .com / in-in-in-in-translate ") so that this page can only be opened by those who know the way to it.
In-context will only be connected to this page.
After a year, we created a mirror website, a full copy of our site but with a different URL where translators can do translations as if it were your real site.