Removing the ability to cancel the appointment is a simple fix.
In your email script, uncheck the box that allows your customer to cancel, so they will only get the option to confirm, or reply to your email address. You can add directions to your email for what your client should do to reschedule the appointment, as shown below:
For SMS, go to edit script, then in the 1st box, remove text back '5 to cancel' entirely from the message that gets sent. They will then only be able to confirm, or request to be contacted by your office to reschedule.