Audacity can be made to do this but it would take a lot of programming work. I suspect that (if not SoX) a VB/VC++ app, from scratch, might be easier to write than hacking the Audacity code. If you want to hack the Audacity code, most of what you need can be found here:
https://forum.audacityteam.org/t/unattended-command-line-processing/15543/10
where I have made code available which allow this kind of operation.