OK, so in effect you're doing a 'proof of concept' of the video quality and viewing/playback features on a small collection of IP HD cameras, with any large-scale implementation design deferred till later.
Let me try to make some suggestions, and ask others to chip in as well.
for now just need the 10 cameras on a single NVR at one location
That makes things easier, in the sense that you may not have to integrate much with the existing network infrastructure, which for the observers here is an unknown quantity.
But is part of what you must do the ability to view the NVR (Live view, playback etc) at a location remote from the cameras, but presumably still via the hospital network?
If so, that precludes the ability to create an isolated network, where you could choose and use your own IP addresses for NVR and cameras. And on the assumption that the premises cabling is run back to wiring closets, you could still potentially make use of just the cabling infrastructure for an isolated network.
Much the simplest solution if you want to make use of the NVR you have is to convince the IT Department to assign you an IP address for each device you need to connect to the network (ie NVR and cameras), cable these all into your switch (which is a Gigabit layer-2 POE switch with some IP facilities including a web admin and well suited to your task), and assign you a physical port on the wiring closet network switches for uplink to the main network.
I think you've figured that if you use a Hikvision POE NVR, it has a built-in separate network via the POE switches where you could set up cameras independent of the hospital network, and only attach the NVR LAN port to the hospital network. That could certainly be a 'Plan B' if the IT Department doesn't change their stance.