@Faye73
"The whole booking money" is the money you already refunded plus the Airbnb commission you probably didn't. The whole amount you receive from Airbnb is not the whole amount the guest paid.
Despite the circumstances, your only refund due to your guest would have been in accordance with your refund policy. If a guest requests a refund there will be required a cancellation - which your guest should initiate - your agreement to a refund (which you should not agree to apart from only which your refund setting allows).
Refunding your guest directly would not avoid any bad review.
In the circumstances, I would be inclined to inform Airbnb about what happened, explaining you were not aware of their involvement with the refund process, that you have already refunded the guest in full and that they may receive a request for refund from your guest. There is a chance you might be penalised by a double refund if Airbnb are not aware of the existing refund.