Is there a physical device that can provide VPN-only wifi connection, so that a laptop or wifi-only ipad (say) which were to connect to it would not risk ever exposing its IP?
You can configure your router to route all traffic through a VPN. It's a standard setting in all routers.
That is incorrect. Many, many routers in fact do not have a setting to route your traffic through a VPN. My Linksys for instance does not. Famously, people flash DD-WRT or Tomato on their routers to enable that.