The column has to be in the P or N position for the key to turn, mechanically, regardless of the switch being there.
I do not know how the switches on your new shifter work, but the two pairs of wires (listed previously) have to be connected to each other to work by the switch.
Basically, when you put the shifter in reverse, the switch needs to close the circuit and connect the blue and green wires to each other so your backup lights will come on.
Concordantly, the shifter's neutral safety switch has to close the circuit between the black and orange wires (when in P or N, or maybe just P, depending on the shifter, for the starter to turn) IIRC. It has been a while since I messed with this stuff.
The part in italics is incorrect.
OK, I was wrong...The blue and green wires ARE for the back up lights, but the black and orange wires are for the computer to know status of the shifter, and have nothing to do with the starter.
The wire you need is the purple (or red) wire on the ignition switch on the column. I will look on mine later today to try and verify the location. The neutral safety function is totally mechanical, as in the key can only be turned when the column (shifter) is in the correct rotation.
Honestly, the very best solution is to leave the column linkage hooked up.