You're boned. Then most systems including Ethereum are based on the assumption that the miners aren't majority controlled by an adversary. That may or may not be a sound assumption.

The whole idea is kind of predicated on whoever you're worried about attacking you not wanting the information to get out more than they care about getting to the person holding the dead man's switch. If they are more concerned with getting to that person than with whatever information the person has threatened to publish no level of security on the switch matters it just becomes part of the cost of getting to the owner.