Question about Logitech G G502

All right, without additional software or admin rights for the installation, this is of course a bit tricky. Within the Logitech family, the Logitech G600 may be of interest to you:
Logitech G600 MMO (wired)
However, I'm not sure whether this can also be configured with Setpoint & Options or whether the G-Hub software is required for this. Maybe your IT department can be persuaded to add G-Hub to the software catalogue, as you are already halfway integrated with Logitech with Setpoint & Options anyway.