I'd go over the metal with a wire wheel to remove what ever rust can remove before annealing it.. I do that just because it seems like the right thing to do!. No need to go hard and rough,,just a fine to med wheel with a light coating of oil on the metal and they clean up pretty well.
Take some patterns, lifts and/or pics of the engraving before the polishing especially if it may be lost during the process. The engravers appreciate that.
Do the annealing or have it done.
Then procede with your polishing to clean and square up the surfaces and remove any pitting.
Maybe the engraver would like to do the polishing along with the recut so as not to disturb and loose any of the original pattern or lettering.
Best to ask him/her. Some do,,some don't,, like to do any polishing & prep work.
I prefer to do the prep work myself, but everyone is different.