This is an exactly what you’re looking for, but it might work for you. You can go to the VireoLink website (link below), enter the link for your YouTube video, and generate a new link. When you use the video link you generate, nothing except your video will show. There are no pop-ups or advertisements or “next” videos showing. It’s completely safe and it is designed for parents and teachers who want to show videos safely.
https://video.link/
This is a link to a YouTube video:
https://youtu.be/cjtnJf5mGZ8
And this is what it looks like on VideoLink:
https://video.link/w/i6fCb
I just noticed that there is a link to download your video. It uses another program, and I haven’t tried it, but it might work for you. Look just below where the video is playing.