That's exactly what I plan to have done. I wasn't sure if I was going to stamp something on the back of the headstock to make is obvious or put something in the cavity.You do you, but it would be cool if you put in the control cavity or under the truss rod cover or something that it's not an ESP.
At the end of the day, you'd have to have half a brain cell to buy a refinished Edwards and think you actually bought an ESP custom. Actual ESP's have so much more markings on them, different serial, and even a different paint job to anything I would refinish to. If for some reason it were to be ever sold, it would sold as refinished Edwards, not an ESP.