If those wires are over 0.5mm in diameter you may have to crimp those to short lengths of 0.5mm wire and then terminate those on the IDC
If the insualtion is thick and heavy you will need to strip back the insulation as dispite IDC being insulation displacement connection, if the insulation is too much the connectors would not be up to the job of cutting though the insulation or distort away from the wire so if it does contact it may be a losse fit or suffer from HR dis'