Looking at the manual for the Korg, it appears the SV-1 can send and receive on only one channel, and I don't see any mention of splitting the keyboard to play two different sounds at the same time, so I'm thinking there's no way to do what you want unless you use a computer or smart interface box as a go-between, as follows:
Korg SV-1 <==Channel1==> computer/box <==Channels1,2,3==> Hammond XK-2
The channel numbers shown are completely arbitrary, so you could use different ones if you want, but the Korg can send/receive one channel (and uses channel 1 by default unless you change and save the default), and the Hammond can send/receive three channels (upper manual, lower manual, and pedal keyboard).
You would turn off the Local Control setting of the Korg so it wouldn't make any sound when you play it; instead, it would send its Note On/Off events to the computer or smart interface box on channel 1.
You would use a program such as a DAW on the computer-- or configure the smart interface box-- so that it takes all the Note On/Off events coming from the Korg and divides them up into two, three, or four zones based on the Note values. In a DAW, this is done using a feature that's often referred to as "MIDI effects."
You would then have the computer or smart interface box send the Note On/Off events for each of the two, three, or four zones to either the Korg or the Hammond.
For example, let's say you've split the Note events into four zones as follows (I'm assuming the Korg has 88 keys):
The Korg sends A0 to C8 to the computer/box using channel 1 of the Korg's MIDI OUT port.
The computer/box splits A0 to C8 into four zones:
A0 to B1: Zone 1
C2 to B3: Zone 2
C4 to B5: Zone 3
C6 to C8: Zone 4
The computer/box sends each zone to either the Korg or the Hammond:
Zone 1 is sent to the Hammond's Pedal Keyboard using channel 1 of the Hammond's MIDI IN port.
Zone 2 is sent to the Hammond's Lower Manual using channel 2 of the Hammond's MIDI IN port.
Zone 3 is sent to the Korg using channel 1 of the Korg's MIDI IN port.
Zone 4 is sent to the Hammond's Upper Manual using channel 3 of the Hammond's MIDI IN port.
I've used International Pitch Notation, but the computer/box would presumably use MIDI Note values. And this is just an example; you wouldn't need to split the Note events into four zones (that's just the maximum number that these two keyboards could potentially use), and you wouldn't need to use those specific channels.
The only possible wrinkle in the above scenario would be if the Korg takes the MIDI events coming in over its MIDI IN port and automatically sends them out over its MIDI OUT port, like what MIDI THRU does. I don't think it would do that, but if it did it would not be good.
If your situation allows for using a computer as a go-between, such as if you're wanting to do this at home, then a computer and a DAW would be an ideal solution, since you might not have to buy anything else (if you already use a DAW for recording).
But if a computer isn't ideal for your situation, such as if you're wanting to do this on stage, then a smart interface box might be the better solution. I don't have any hands-on experience with any, so I can't recommend a specific one as being best, but some of the possible contenders that I'm aware of are as follows:
- BomeBox, with Bome MIDI Translator Pro software (purchased separately) for programming the zones/routing.
- An iConnectivity MIDI interface such as mio2 (if Note events can be filtered and split by their Note values).
- MIDI Solutions Router (if Note events can be filtered and split by their Note values).
I'm sure there are other contenders, but those are a few you can look into further.
Another possibility for an on-stage solution might be to use an iPad for the routing and event processing, but that would require an additional interface so you could connect the Korg and Hammond to the iPad at the same time. And if you'd need to buy some kind of interface anyway, it might be better to stick with a smart interface box.
Or you could use a laptop, instead of a desktop computer, if you need better portability for the road. Companies make laptop stands for musicians and DJs.