Is there a method in AppleScriptObjC (not System events) to send a copy (or cut or paste) event to the active application?
No. Generally speaking, there’s very little you can do to other apps.
That’s what I suspected.
The Cut and Copy actions wait until the clipboard changes before proceeding.
You can call KM Macros and Actions from AppleScript, as well as call AppleScript from KM.