It's a giant red flag that the guest is flip-flopping on his reservation. Be careful when accepting this reservation again.
You cannot refund him any money and you should not offer to do so. The cancellation policy is in place to protect you as a host. If the guest wants to contact Airbnb and try to renegotiate his refund, you can encourage him to do so. If anything, they are likely to offer him a credit toward another rental.
Assuming that the guest cancelled within the 5-day period of the Moderate cancellation policy, you will receive 50% of the original booking amount. That means, if you want to rebook him and provide him a discount for having paid you 50% already, you can offer him a discount on a new booking by sending him a special offer once he inquires about booking dates. You can make the special offer as low as $10/night.
Good luck. Hopefully the other inquiry has already responded and you can tell the original booker you are not available.