To limit a user's access and effect upon your Shopify integration, disable the "Export All" permission in their User's Role.

Any User with a Role that has "Export All" (found in the Settings group of Role Permissions) disabled will not be able to action the "Export Products from Unleashed to Shopify" or "Export Stock on Hand" options in your Shopify integration's Manage your Data tab. 

For more details on managing User Role Permissions, see Role Permissions.