With YouTube videos, one option is to load the videos from www.youtube-nocookie.com instead of www.youtube.com. However, that could still load some cookies, though I think those are necessary for the videos to play properly. I'm not sure if Vimeo has a similar no-cookie option.
If you have any video tracking implementation, then you'd want to block the video providers' API libraries till consent is given. For YouTube, that means blocking calls to www.youtube.com/iframe_api . However, if there are other non-tracking-related programming being done to the videos that do rely on those libraries, e.g. programmatically controlling the playback quality, then you're stuck with needing to load the libraries nonetheless so that user experience is not affected.
