If you set a static IP address in the device, the router should simply notice that something is on the network when it tries to send traffic. That is completely different from a reserved address that still uses a DHCP handshake with the router. So, yes, you don't touch the router settings.
Since there's no DHCP negotiation, you have to tell the device several other things about the network as well as what address it should have: you have to tell it where to send traffic (gateway, usually the router address), where to find nameservers (usually the ones provided by your ISP, but you can choose others if you prefer -- and you don't need any if you don't want the device looking up other computers by name), and what the netmask is (for a home network this is usually 255.255.255.0, meaning only the last octet will ever change). This information can be obtained from the DHCP negotiation that was done to get the device on the network the very first time, so it could be filled in automatically by the setup software.
But the user has to pick an address to be used for static addressing that won't ever be assigned to something else by the router, so it does require some knowledge about the user's home network.