Instead of capturing videos from Youtube via screen recording software, it's better to download them directly with downloading tools. This way you can get better quality/filesize ratio because no re-compression is applied. I'm using "Freemake Video Downloader" and it works perfectly, just tested it.

Of course it's in your own responsibility what to do with those videos and respect any laws. Generally spoken, re-uploading them on Youtube or anywhere else is not a good idea unless they're marked as CC by the uploader (in which case you must give credit to that person in the video/description) or are public domain (for example NASA videos etc.)