How to disabling Urban Airship's notifications

I would suggest disabling Urban Airship's notifications and handling the Push events manually.

To disable Urban Airship's notifications, override BasicPushNotificationBuilder:

BasicPushNotificationBuilder nb = new BasicPushNotificationBuilder() {
    @Override
    public Notification buildNotification(String alert,
            Map<String, String> extras) {
        return null;
    }
};
// Disable notifications
PushManager.shared().setNotificationBuilder(nb);

Then implement an intent receiver according to the documentation here, and create your own Notificationto meet your spec.