You are approaching the right wiring but there are still a few areas that need attention.
You are drawing a set of four lights that are two way switched.
However in your original post you wanted a two way key switch, in general two way switching for normal lighting is not integrated into the key switch. So it would be useful to know which method is required.
Key switches tend to be available as either double pole or two way, but usually do not use the two way function of the switch for emergency lighting.
Assuming you want two way switched lights and one emergency light with a separate key switch for testing:
The Emergency light needs a permanent line; this line needs to be broken by the key switch, however it cannot break the neutral to the other lights or they would stop working during the test, which is not recommended.
The neutral is not involved in the two way switching or the key switch.
Perhaps if you were to work out the wiring so that the neutral is not switched at any point and the key switch only switches the permanent line to the EM light.
Also check the type of switch you would use to provide normal two way switching for the lights and use that switch in both two way switching locations.
You have the correct switch at the top of your diagram labelled 2-Way SW.