You can either use the actual YouTube Website from Web browser or here is how to download older app versions to your older iPad.
If you need older versions of apps that have moved on to iOS 10 and later, tap on my link below and choose the method that best work with your current situation.
CAREFULLY read and follow ALL directions.
All three of my procedures/solutions work!
Downloading Older iOS 9.3.5 Versions of A… - Apple Community
Apps may or may not have older iOS 9.3.5 versions still available from the iOS App Store.
Older versions of YouTube still exist in the iOS App Store.
There are three ways to try/attempt to get an older version of an app. Pick the method that works best for your situation/circumstances.
Also, I would STOP using that 2-2-1/2 year old Safari web browser, as it is, probably, not safe and secure to use any longer, and seek out a third party web browser that is STILL currently being updated and STILL being supported on iOS 9.3.5.
Heed my advice on this issue in my above link.
Good Luck!