mailchimp no more supporting with Shopify, so better to use klaviyo
It's been quite a while since you posted this and you might have figured this out already. In any case, I'd still be happy to help.
At this moment, it is not possible to disable the notifications from Shopify. In this case, I would recommend including links to invoices to the Order Confirmation email.
Would this work for you? Please reach out to firstname.lastname@example.org and I will be happy to assist.
Lenka from the Sufio Team