If you want to send a small clip directly to someone without the link.
Go to clipconverter.cc and paste the YouTube link of the video you want to download, it will download the file directly to your phone's Videos folder.
Using the Files app transfer the video to some other folder, like screenshots.
And then send it via Whatsapp.
This will only work if you have Windows Phone 8.1 because it requires a file manager.