You can swap in the other car's EWS/barrel/key if you remove the EWS functionality from the DME.
Trying the donor key without swapping the EWS won't allow the starter to activate (unless you bypass the wiring at the EWS unit), even if the DME has the EWS functionality removed.
Needless to say, removing the EWS functionality from the DME would make the car easier to steal, so the barrel fix is the best thing to try first.