That should be fine. I used Elmer's wood glue but any wood glue would work. The woodworker's wish: "I would that my wood glue would work." The brown paper insulator between the iron and the veneer can be just a piece of a paper grocery bag, etc. Press hard with the iron all around and keep it moving. If it's a large piece, work so that any ripples in the veneer can be worked towards an edge and out. If, after you're done and before the piece has any finish on it, if you see a place that didn't bond, you can iron it again.
BTW, Mrs. likes the Firestone and thinks it's pretty!