If the engraver is qualified to work on a high quality shotgun he or she should be able to answer your questions in detail and have the proper contacts for the non-engraving aspects of the job.
"Disassembly, annealing and polishing would be mandatory in my experience." I agree with Steve.
As to rehardening, some guns have CCH only for looks and are made of modern high strength steels. Again the engraver should know the answers for your particular gun or be networked with other engravers to get the correct answers for you.
Cheers,
Roger
