Can a person put it in their will to not have their cause of death disclosed?

You can put it in your will, but I don't think it would be very effective. first of all, the disclsoure is likely to be made befoe the will is read.  Second, the person disclosing (for example, the medical examiner) will probably not be aware of the will.  Third, how do you enforce it?  It might be possible to have an enforcement mechanism against those inheriting, for example you get the house unless you disclose my ccause of death, but there would be no penalty for anyone who was not receiving anything under the will, and even if it wsa someon who inherited, enforcing it would require someone an interest to sue the discloser, and it might be very difficult to prove who did it.