Well from what the Picture you show the Relay being 5v so you would need a 5v relay that would be on a break out board, converted to NC. SO the pins going to the NVR PCB would be the NC from the relay.. But could just desolder and make that with the Relay you already own.
External relay easier to have 12v relay yes. But there are 5v power supplies around. There are a lot of things you can do. I mean if you are going to use 12v might as well do an External 12v relay so your 2 wires go to relay and then the relay once trigged then sends the 12v to your device.. Now I wish I would have bought the POE Version. I mean I have the first 42xx gen both of them are NO like my first gen 5232... must be a reason they went 1 NO and one NC.