Well I've devised a way for myself to do this, and I'm still interested in knowing how you guys would do it. I'm sharing in case it would help someone in my position, or to help you better guide me for next time with alternate solutions.

This procedure only works for adding a second language, not a third/fourth/+ (because the language selector would see it...however if someone visits the website with a regional setting or IP matching the second language, would it still have switched automatically to the non-translated pages?) : 

1. Remove language selector from Copyright bottom bar 
2. Install second language in website
3. Go to each page, add the language code in URL (e.g. for French, go to https://sitename.com/fr/pagename) to get to the second language version
4. Translate each page this way
5. When ready to make the pages really accessible to humans browsing, add a language selector

Creating a new site or new pages and then switching branching through redirections is not really an option since it would lose history of visits/analytics/ranking/SEO.

Isn't there a better way to do this? I'm all ears :-)