Remember, Luxe is an upgrade to the Base subscription. After you've been billed for Luxe, you can cancel your Luxe upgrade without canceling your BoxyCharm subscription.
To do so, visit your Account Preferences page and find your Luxe upgrade under the "My Subscription(s)" section. Then, next to your Luxe subscription, click the "Cancel" button and follow the steps until the cancellation is confirmed. Your Base subscription will remain Active.