Can I use a commercial LAN cable to PLZ-5WH2 series instead of the optional parallel operation signal cable kit (PC01/02-PLZ-5W)?

No, you cannot. The cable kit (PC01/02-PLZ-5W) uses the typical straight LAN cable, however the split toroidal core is attached to the cable kit.
The performance of PLZ-5WH2 series is not guaranteed without this core.