No, the nesting boxes don't need a perch, but they can be helpful. I don't have perches on mine but my chickens do perch on the front lip (which holds the nesting material in).
I was going to recommend a simple guillotine-style door like the one I built:
The lock (just a swiveling wooden block) doubles as the stop that holds it open. The nice thing about this door is there is nothing on the outside for predators to hold onto to slide it open.
But being that your...