Just be cautious of giving the class access as the responsibility will now lie with you on making sure inappropriate content isn't viewed by students on your device. This will also mean that in future you won't need to ask for permission again, presuming the unblock remains open for you. In the case of schools using Google Classroom via the G Suite, this is very easily done and can be for specific users, browsers, devices, and more. Often it can be easiest to go to them directly to have your machine unblocked for access.

For most schools there is going to be an IT admin in charge of the YouTube block.