other than enforcing what is probably a disproportionate punishment and consequence
I don't think the consequences are disproportionate.
You warned your son that he needs to stop or he would have to go without his tablet for a week. He didn't stop. Now he has to do without it for a week.
A week isn't that long. Not watching videos for 7 days is not going to hurt him in in any way. And frankly, I don't think it will hurt him to not be able to use his tablet at school (I'd be very interested in what a nine-year-old is being taught at school that requires a tablet, but that's off topic). You could always tell the school that your son can't bring his tablet to school for a week. The school should have a protocol for such cases. I mean, what happens when a child breaks his/her tablet, or brings one with an exhausted battery? The teachers should be able to deal with that.
If tomorrow I "soften up" and allow him limited use of the iPad, am I undermining my parental authority?
I agree with anongoodnurse that you probably wouldn't undermine your authority. Explaining why you made a mistake will also make him see that admitting one made a mistake is not a sign of weakness.
Still, I don't think you made a mistake, and therefore I don't think you should admit to one.
for use only in class - but as I am not always present I may not be able to enforce this behaviour
This is the problem with you giving him the tablet for school use. If he's anything like my nine-year-olds, he won't be able to control himself and he'll use the tablet for fun when you're not there. Then he'll lie about it because he won't want to suffer further consequences.
To pick up on anongoodnurses example with the revoked driving license and you only being allowed to drive to work: Wouldn't you be tempted to make a quick detour to play some pool on your way back from work with your buddies, even if you weren't supposed to? And it's almost no detour at all, and nobody will be the wiser, and you can always say you were just there to pick up some groceries for dinner in the shop next door if your car does get spotted, and that's true, you do need to pick up groceries, and anyway, who gets hurt by that...
One big problem with tablet availability for kids is that they're just too interesting for the kids to reliably muster enough self-control to put them aside. It seems to me that learning this skill is very important, even more so if your son has access to a tablet during school hours. So suffering the consequences of not being able to stop when he's told to stop seems like a good thing here. Maybe next time you tell him to put it away, he'll put it away. Then maybe next time you tell him that he has forty minutes to play with it, and to set an alarm to remind himself, he'll do that. Then sooner or later he might start doing it without you having to remind him every step of the way.