Lawyers representing Equatorial Guinea President, Teodoro Obiang, wanted the documents for a civil action against those they accuse of planning the coup.
Sir Mark Thatcher admitted unknowingly helping to finance the coup bid in a South African court earlier this year.
Briton Simon Mann is in a Zimbabwe prison for his part in the coup.
He is one of those being sued by Obiang.
After legal proceedings lasting a year, the Guernsey Court of Appeal overturned a previous ruling that papers showing the details of those paying money into a set of accounts on the islands should be released.
Mark, son of the former British Prime Minister Margaret Thatcher, was given a suspended jail term and fined after agreeing a plea bargain to help South African investigators.
Another 64 suspected mercenaries travelling with Mann remain in a Zimbabwe jail.
Fourteen others are in prison in Equatorial Guinea, after being found guilty of trying to topple Obiang.
The leader of the advance party, Nick du Toit, was given a 34-year sentence.
The conduct of the trials in Zimbabwe and Equatorial Guinea were criticised in the West, amid allegations of torture and forced confessions.