Is it possible to have an approval workflow where the approvers do not have access to NS? For example, if the approver replies to the NS email notification with the word "Approve", then the record will be approved in NS.

Something like this would probably work for you via Advanced Approvals Feature -

Yes, this can be achieved. Years ago, we began offering a bundle that can accommodate approvals from either from buttons embedded in email templates or within an advanced PDF/HTML templates: https://extendtech.net/netsuite-email-pdf-webapprovals/ So, it's definitely acheivable. 🙂

The ad on is called “Approval Workflow Automation” on Squareworks.com

Thanks everyone. I'll look into them.