I don't know what a siri proxy server is. You will probably need to dig in its documentation to see what kind of authentication it uses. Maybe it is key or certificate based and you need to create and copy keys. Another possibility is a vpn tunnel, which would also involve certificates.
If by wifi, you are referring to your own wlan, then you can use fixed IP addresses or MAC addresses to filter access. If you meant the client may be using public wifi to access the network, then you can't. The wireless router will probably be nat'ed
so there will be several devices with the same IP source address.
You will either want the server located on the edge or in the DMZ to prevent unauthorized traffic from existing inside your LAN.