I don't have a D4, but as far as I know, it should be possible yes.
ShutterSnitch doesn't connect to the camera. The camera connects to ShutterSnitch.
Look at it like two telephones. ShutterSnitch is a telephone waiting for a call. When you enter a collection, you'll see an IP and a port number at the top of the screen. That's the "phone number"*.
So first you have to make sure that both "phones" are connected to the network so they can reach each other. In your case you're doing that with a router, and it sounds like you've got that down.
Second, you'll need to set up your camera to know who to "call" when there's a new photo that has to be transferred. You do that by telling it the "phone number" of the FTP server (When you enter a collection in ShutterSnitch, it'll start an FTP server - and show you the relevant numbers at the top of the screen).
In order for the camera to read and write to the collection, it'll also need to supply a username and password. The default username is snitch and the password is the super user password you set up when you first launched ShutterSnitch. Both of these are case sensitive.
So you have 4 things you'll need to tell the camera: IP, port, username, and password. If any of those are wrong, the camera won't be able to establish the connection.
The D4 connection wizard doesn't ask for the port ..so it could very well be that. If you go into your ShutterSnitch settings, the second field from the top is "FTP port" - change that to 21 instead of 26000. 21 is the default port that the D4 picks. Then try taking a photo and see if that makes the camera connect and transfer.
* = Well, to make this analogy better, the first part of the IP is what planet you're on, the second part is the country code, and the Port is the phone number. But let's not dig too deep. Shaky ground.
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