As you have said that you have URL of the deleted YouTube videos. Then there is a solution for you:
Go to archive.org and then paste the URL of the deleted YouTube videos in the search field of the Wayback machine and click on browse filed.
This will find the deleted YouTube video. You can then download it from the there and then save it on your computer.
Another solution to recover deleted YouTube videos is to contact help YouTube support help team. Simply log-in to your YouTube channel and go to the bottom of the page and click on Help> Need more help and then click on Get creator support. Select the suitable category as per your issue and then click on Email Support. You can also click on “Contact the creator support team” link as well.