Can't see any way of doing it through Safari. The video manager doesn't seem to be there at all. Have you tried Chrome on iPad? It could be that Google's own apps will allow more control. I can't explore because I don't have Chrome on my iPad or iPhone.
If it's one of your own uploads that you want to delete, here's how it's done using the app:
Make sure you're logged in. Then select"My Channel" at the left, then "Videos" (or if visible, just tap "Uploads" at the left). You should see the videos you loaded. At the right, there are three dots. Tap them and select "Remove Upload".
To remove videos from History, this is what you do:
Tap History - the trash bin at the top right - OK
Delete them from Watch Later (Favorites is about the same):