Although its rather tangential to the game mechanics,
With the Captain's log book, the crew can determine that the destination is Niel in the Far East. The log mentions receiving more gold upon its delivery, but makes no mention of the contents of the trunk, which has a series of locks keeping it closed.
As to proof, there is no other evidence pertaining to the captain's murder, other than the sailors knife, which is as common as a cockroach.