I would forward your confirmation e-mail to the property, telling them that you are cancelling pursuant to the original contract, that you do not consent to a subsequently-imposed cancellation fee, and that if any such fee is imposed you will be disputing it with your bank.

Then cancel. If any charge is made to your credit card, dispute it ("Service not received."), enclosing copies of the two e-mails, and any response by the property.

In such a clear case, the property might not contest the "chargeback" dispute process.