Quite simply, is there any way to temporarily prevent an NPC that uses Shouts, like a Draugr for example, from using them?

Spellcasting can be stopped by wiping out the creature's mana supply, but shouts don't use mana...

I suppose since Draugr basically only use Unrelenting Force you could just do a removespell, wait, addspell on them. Other than that I can't really think of anything.

Some of the high level Draugrs use the Disarm shout, which is VERY VERY annoying and could even lead to permanently lost weapons because sometimes your weapon would just clip through the level geometry and fall into the void.