But then you don’t need to have a smart contract, simply posting public key of the wallet is enough (to verify the content of the wallet). The contract at most provides an escrow, but even that isn’t really the case since presumably the originator has the key to pull the money (since he knows the secret key).

Proving that an encrypted text has the private key is possible for some encryption schemes through zero knowledge proofs, but I guess not in this case in particular.