I get the impression that the OP wants to run software on a local computer for their primary data handling to extend the data handling that the 6313 console already offers (and maybe to have the flexibility to change software if the first choice program loses its appeal). In that case,
1. The choice of software would be probably from Weatherlink for Windows (dated UI but still perfectly functional), CumulusMX, Weather Display or weewx. Pros and cons to each and also depending on available computer and OS.
2. If the 6313 console is already uploading to weatherlink.com then this second receiver can be dedicated solely to local data handling and so doesn't need to upload to wl.com.
3. So in this scenario MB Nano would possibly (?) be overkill and even an Envoy + a WFL DIY logger would provide a simple data feed to the computer, probably with a serial-to-USB adapter. so all the data handling for this unit would be handled in software on the computer.
But ultimately it depends on what the OP wants in detail out of the system, what local computer they might have in mind, budget etc.