For future reference always call AirBnB first. While the booking will be ultimately cancelled, it's better to give AirBnB a head's up. They tend to take the side of whoever calls in first. Secondly, they'll either cancel on your behalf in which case, it's not a host cancellation, so it's essentially off the record. I have my guests copy/paste my house rules and message them to me via AirBnB's message platform prior to arrival. This ensures that they've read them and holds them accountable. AirBnB tends to look at violations of house rules in these cases and simple open/shut cases.
Recap
Call AirBnB first to get ahead of the power curve.
Discuss options and alternatives.
Get AirBnB to contact the guest and cancel on your behalf.