You need to:
1- generate a new address/wallet
2- announce the address to other party
3- transfer funds from the original utxo to new address
this method is not good at all because first of all it forces you to create an unnecessary on-chain transaction and pay fees, specially nowadays that fees are shooting up again.
secondly it is not reliable since it can be faked. you have no way of knowing whether the sending address or receiving address belong to the person trying to prove ownership.
Note: Signing a message with your private key is not safe because you need to disclose the corresponding pubkey (which your address is its RIPEMD-160 hash).
you don't exactly disclose your pubkey, not directly anyways. you only reveal your signature and your public key can be found from that. and more importantly you can NOT call it "not safe" because it is perfectly safe, as safe as millions of translations that have been made so far. in other words just because some day ECDSA may be broken doesn't mean it is not safe today.