Put a small amount of RAM in the keyboard. Trigger it to capture text when the copy command is issued (probably would have to be USB - can you send signals the other way on PS/2?). Flip the KVM. Send the proper keystrokes when the paste command is issued. Unless the keyboard briefly loses power when the KVM triggers - which seems likely. Eh, how hard can it be to add a battery?
The trick there isn't the power, but rather figuring out how to tell the keyboard what text is selected. You'd need special drivers to do a local copy, and send the text to the keyboard.
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