If you are up for some hardware tinkering, you might be able to modify an existing KVM switch to add remote control. I had a KVM switch with a wired button (pl

If you are up for some hardware tinkering, you might be able to modify an existing KVM switch to add remote control. I had a KVM switch with a wired button (place KVM out of the way, put small button on your desk). The button was connected via a 3.5mm "audio" jack. I never measured the interface, but I bet it just connected two rings of the jack. Using a switch like that, you can build your own control for it without opening the KVM. Either with an ESP for wifi control (MQTT would be my choice) or a smaller board for USB/serial control (Cortex-M dev board). Short the proper rings via an optocoupler controlled by the MCU and it will behave as if you pressed the button.