Hi Jeff, I appear to have missed your response until now but if it's still relevant, here are some tips. Vimeo has a lot of features to prevent sharing in the professional versions. You can disable sharing and downloading and even decide which specific domains the video can be played on, so it's a very safe platform in this regard. The options are behind a pay wall, so they may not appear if you're using the free version of Vimeo.
I even tried one time to retrieve a video through our page source code (on a page that had one of our embedded Vimeo videos) just to see how safe it was and I definitely couldn't hack it - so short of serious hackers, I wouldn't be too concerned. š
The most important thing is that you do not share the link to the video. For example, if you wanted to send an e-mail to a student with a direct link to a video hosted on Vimeo. This link can be used to rip the video - just Google "Vimeo ripper" and you'll see there are tons of pages where you can easily steal Vimeo content, but you do need the direct link to the video.
So long as your video is embedded into another page and this is the only place that anyone views it, you're safe from everything short of screen recorders and talented hackers. A student could record their screen and play the video in its entirety and thereby rip the video. But to my knowledge there's no way to prevent this on any video hosting platform at all.
As of now, Vimeo and YouTube are the video hosts that are most likely to be targeted by hackers and rippers simply because they have such a massive share of the market for video hosting. A smaller provider with similar functionality may theoretically be a safer bet just because they are less interesting to the people who produce software that can compromise the security measures. In my opinion though, Vimeo is safe enough and no matter what you do, there's always a risk once the content is online. Vimeo reduces this risk by a lot and I think it's safe to say that there's a general consensus about it being safer than YouTube.