Can I delete the range switch on the side of a 4L60E in a square body swap?

Here is what the documentation says. Each point links to its source; details depend on your exact computer, harness and transmission.

• 4L60E: When installing an aftermarket case-mount shifter on a 4L60E, it is not necessary to remove the transmission's Manual Lever Position Sensor (MLPS). (Lokar, Inc. (via manuals.plus))
• 4L60E/4L80E: Truck/SUV 4L60E and 4L80E transmissions have a factory reverse-light switch on the shift detent rod on the driver's side, and the same switch incorporates the park/neutral switch; swap harnesses wire their reverse-light wires to this switch. (Painless Performance Products (via Scribd mirror))
• P01/P59; Gen III LS; 4L60E/4L80E; 1999-2007: PSI standalone harnesses include an orange Park Neutral Signal wire that is explicitly NOT a neutral safety wire: it is a PCM strategy signal that goes to ground when the transmission is in Park or Neutral (used for idle/shift strategy), and must not be wired into the starter circuit. (PSI Conversion / Performance Systems Integration (via SlideShare))
• Sources differ: Contrasts with forum advice to delete the range switch entirely: removing the switch also removes the PCM's park/neutral strategy signal used for idle control.

Confirm against the instructions for your exact parts before wiring. More: Other wiring in our tuning guide.