@Frankenscript you definitely shouldn't need the "extra router", because I am running that exact configuration (with the physically separated networks) without one. General guidance is that VLANs will do this easily as well, but I wasn't ready to tackle VLANs until I learn more about them.
I am using the HP-1920-8G-POE+ switch where you show a POE switch to power your cameras, with
Blue Iris connected to one of the ports and with a fixed 192.168.1.5 IP Address. Since my cameras have so far always wanted to be on the 192.168.1.x subnet, Blue Iris can scan for each new camera that I connect. On the camera side I tell them all 192.168.1.1 is their gateway, and there isn't a device with that IP on that network. It works because Blue Iris is connecting to each camera, and the cameras don't need to connect to anything else (the Blue Iris machine is configured as their time server).
The only nuisances are 1. this approach does consume a port on your POE router that maybe a different configuration wouldn't require allowing an addl camera and 2. to access the camera setup web pages, I have to remote desktop to the Blue Iris machine.
But it's easy setup if you are a network novice, and I feel it is secure from a lot of the threats you hear about these cameras and botnets etc since the cameras can't electronically reach anywhere but the Blue Iris machine. That security came with a $24.95 price tag as I needed to buy a USB network dongle to get a second network port on the laptop I started out with. If yours is a PC, network cards are cheap and you don't even really need a great one.
Try your setup, minus the second router, you'll be golden.