If you cannot afford to lose or have them stolen, I assume you keep them in your carry-on rather than check them when flying, so no need for TSA approved lock except when at the hotel. Perhaps a better option is keeping a secure lock, not TSA approved, in your bag and put it on after flying?
No lock will deter a determined thief, but to guard against the casual snooping or kleptomaniac maid, a solid lock with unique key should do OK. Could even get a cable lock to lock the suitcase to a fixed object in the room to avoid having the whole suitcase walk away if the documents are that important.
This has always worried me: thieves somewhere will always get their hands on (copies of) master keys. Or simply are masters on picking locks.
When I travel with big amounts of equipment, I simply plastic-wrap my luggage. That must really discourage thieves to try to open them up. And if security really wants to open it, they don't have to destroy my lock: simply get it re-wrapped.
Why for idiots? I use them on all my luggage. I occasionally find the notification from TSA that they opened a bag. I have a guitar case with a TSA lock on it. They've inspected that.
Never had anything stolen.
If you use a non-TSA lock they will simply cut the lock off and may or may not damage your bag doing it.