It is not possible to disable specific SMS notifications while still keeping the SMS option enabled. You can fully disable the option to collect phone numbers for SMS updates by going to Settings/Checkout & Settings/Notifications. By disabling the option, customers will no longer be able to sign up for SMS notifications.
Trevor | Community Moderator @ Shopify - Was my reply helpful? Click Like to let me know! - Was your question answered? Mark it as an Accepted Solution - To learn more visit the Shopify Help Center or the Shopify Blog