When we were looking for a back door, we eventually decided against one in the door, and fitted it in the wall under the sink instead. There is then a tunnel built in to the unit under the sink which the cat walks through, and then she just has to duck under the door at the front of the unit. The really *big* advantage of this, is that you can have a cat flap at both ends of the tunnel - which massively reduces draughts.
We initially went for this approach when adding a cat flap to our nicely insulated door was going to be expensive, and only included one flap. After a few months of windy weather, we added the second flap.