What is the best way to go about doing this?

I have a region similar to Blackreach that I want to disable player shouts from until they complete a certain task. Reason being, some of the shouts would really trivialize some of the challenges I have in mind, mostly in terms of navigation puzzles. I don't mind the player having such shouts after the challenges are completed the first time though.

There are papyrus scripts that can increase cooldown, but it is my understanding that this only triggers after a shout is already made and it isn't really an on/off sort of thing. I basically want to have it so the cooldown effect is on 24/7 while the player is in my region, at least until they complete the task that enables shouts again.