Here's the door, inside and out. I've taped on the frame outside at the lowest height it could be without straddling the moulding. The exterior is covered and on a protected side of the house so I don't have to worry too much about weather proofing, but it does get cold.
Really can't think of any way to help you decide. Fire door blank and keep the old door would probably be better than butchering that one. I would expect a cat to be able to get in and out of a cat flap where you have it taped now though, unless it's particularly small.
Here's the door, inside and out. I've taped on the frame outside at the lowest height it could be without straddling the moulding. The exterior is covered and on a protected side of the house so I don't have to worry too much about weather proofing, but it does get cold.