This is the best use case for blockchain. Put the secret on the blockchain and show others that transaction. Since it's on blockchain, no one can deny your claim about knowing the secret. This is why blockchain was invented.
Before blockchain, I was miserable. There was no way for me to prove to my girlfriends that I knew a secret, without telling the secret. Now with blockchain, my life is so easy - I just show them the blockchain transaction and they know that I know.