As Maximus points out: The answer can be found here: ConEmu Documentation > ConEmu.exe command line switches
This shortcut target:
"C:\Program Files\ConEmu\ConEmu64.exe" /cmd
will start Minnty hooked up with Cygwin if you create a proper Task for Minnty inside ConEmu (Settings > Startup > Tasks), with this Command:
C:\cygwin64\bin\mintty.exe -