Sound routing application

So this is not in-essence FreePBX related, only by the fact that one of the systems it wishes to bind in the solution, uses FreePBX as the Local SIP PBX…

Some of my agents who use the SIP IP phones, also do have desk-phones running on a parallel-running Siemens HiPath.
It’s obviously not practical to swap around their headsets between one deskphone and another one…

Their workstations however are running SIP clients (MicroSIP/Windows or Linphone/Linux). Mainly for the purpose of caller-display and CRM integration; but they are entirely capable of handling voice calls too;

So I have been imagining, that (by the virtue of a handset splitter) I can deliver the deskphone two-way audio to their workstation at the back-audio connectors, where a little program would run, that they would press ‘a button’ in, that will deliver the deskphone audio to their headset, connected to the FRONT connectors:

[deskphone]=>[splitter];

[splitter out 1]->[handset] (so that existing system still works without the PCs)
[splitter out 2]->[PC rear input/output]

[PC : routing input/output from rear input/output or from digital application input/output to front connector(s)] -> headset;

The same application would, when another button is pressed, switch over the input/output channels in case the SIP softphone needs them. Say at the press of a button…

That obviously requires switching both in and out audio channels in software [OK so some signal-massaging will have to happen on line-output to the phone, but nothing that can’t be quickly soldered together)

Queries I ran so far have been pointing to JACK for Windows; since it’s a toolkit, some applications that use the JACK have also popped up. I suppose some application for PulseAudio under Linux might also exist. Or the PulseAudio may even be able to handle it without additional applications, so ‘just’ a simple(ish) script… but that’s hardly a topic for this question.

Recording audio on workstations is NOT required nor needed. All I need, is some easily-configurable push-button dual-channel audio-switching.

Has anyone ever heard of such a thing? Any pointers / lmgtfy’s / appropriate keywords welcome.