Hmmm....I would think you could use whatever type of stem you wanted to use. The copper is going to change color. You could always paint the stem to prevent rusting or you could let nature take it's course.

My hubby says steel will be fine. The best way to attach copper to steel is to solder or braise it which will act as an electrolysis barrier and prevent (or reduce) corrosion.

Laura, I think using copper for both will give a great look. The contrast with the steel might distract. The copper will develop a patina, appearing almost like bronze.
Looking forward to seeing your flower! And HTH. Rosie