Writing as an Amara user like you: the whole point of the Amara player is to enable viewers to interact with the subtitles, also in choosing which language they want to view the subtitles in.
So if you want to deprive them of this possibility, what about using a different player? You could still make the subs you want on Amara, then export them and reuse just those in another cc-supporting player.
But I don't quite understand the purpose of this deprivation: even in the hypothesis of a German course where you'd want students to only watch videos with German captions, wouldn't it be better to tell them so, and then it's up to them to follow your indication or not. If they don't, tough titty for them. Whereas if you just amputate the Amara player of its droplist - admitting this were feasible - they'd just have to google the video title to find the corresponding Amara page.
topic name says it all. I'm embeding amara with Vimeo with this code: