I tried it both ways. It seemed a little easier if you did the routing first and then the cutting second.
I did this because I had more area to router than I did to cut. I was little worried that I couldn't cut away too much. My thinking was that I would be better off to leave more flesh on the pumpkin so it didn't become too flimsy.
Here I am doing the routing. It's easy. It's a little sloppy, but it's easy.