I'd cut it. But if you're worried about it, build a support box the length of the tunnel by cutting 4 pieces from an appropriate size board, then use some wood glue and some brads to make a 4 sided box. Place it in the tunnel making sure it fits firmly by using a hammer to knock it in. All you need to do then is affix the cat flap.

ADDITIONAL: I just want to add that if your cat is anything like a cat I had a few years ago, she'll look at the door flap at first with suspicion, then with trepidation as she'd go over and hit it with her paw a few times like she was testing it. After testing it she'd walk away, sticking her tail, and head into the air ignoring the flap from then on. Coming home from work one night we did find her stretched partially through the flap yowling her head off like she was singing holding a catnip mouse, completely high. She only did it once. At least that we caught her at. So good luck with your door flap.