It seems to me that there are two possible scenarios: The hobbyist (H) is the cardholder and he's trying to get a credit for the money he paid you, or the H isn't the cardholder and he used a stolen card to commit fraud.
Either way, I think your remedy probably lies only through Square. You imply, but don't make clear, that the money you received from the transaction is still in your account. Square has or will look at the statements and other evidence you and the cardholder provided and decide or has decided which of you is more likely telling the truth and that party should get the money.
If it's the other scenario and the H used someone else's card and committed fraud, you probably will only get to keep the money if Square provides for protection when a member is the victim of fraud. I suspect, but don't know, that this is doubtful. It's a basic legal principle that a party is not responsible for the criminal acts of a third party. Check the Square terms of service to find out if you're protected. I found the following Square TOS, although there may be others posted elsewhere:
https://squareup.com/legal/ua
I scanned the TOS and didn't see any language regarding the rights of a member who is the victim of fraud.
I wrote above that your only remedy is probably through Square because, while you and the H had a contract, it's not a legally-enforceable contract. It's fundamental that a contract with an illegal subject matter -- here, prostitution -- is not enforceable. That means you can't sue the H and win because the judge wouldn't enforce your illegal contract.
Finally, you might reconsider linking your Square account with your RW identity in light of the following language in the Square TOS: "If we reasonably suspect that your Square Account has been used for an unauthorized, illegal, or criminal purpose, you give us express authorization to share information about you, your Square Account, and any of your transactions with law enforcement."
Good luck! Please post any further questions you may have.