I do have a solution available for purchasers of the Extension Pro Pack and the Pro Pack.
It adds a shortcode which outputs a link/button (depending on the theme’s styles). It has options to set the link CSS class so you can assign it to a theme style. It’ll allow the users which have the core WP
export capability, which by default on the admin role has. You could use a role manage plugin like Members (I think that is the name) to give your user role the export capability. So this sounds like it could work for your requirements.