How to Disable "Update User" in Edit User for Specific Role?

I need to disable the “Update User” button on the bottom of the Edit User page for a specific role. I only want this user to view other member’s profile, without the ability to edit them.

I tried changing the user roles but they must have “edit_users” active in order to view the Edit User page.

I’d prefer not to do a CSS since they can just change that via firebug. Is there a way to just remove the entire button with a php function?