Ok, maybe I’m not clear on your setup. My KVM has a bunch of ports that connect to cables which are mechanically Ethernet cables, those cables connect to adapters that connect to the test machine. We call them “heads” and we use different ones depending on whether we want to connect to the USB or PS2 ports of the test machine.
You must have some manner of high-end version. All the KVM switches I use have the standard ports installed, no RJ-45 types at all.