Lung cancer used to be rare in younger people. No longer.

Christopher Reeve's wife, was 44 and died of lung cancer a year after he passed away. She was not a smoker. It was a tragic loss of both.

Lymphoma also presents in the chest in some, along the mediastinal lymph nodes, and will show up on CAT scan.
In women the ovary can also be a culprit.
This link shows the mediastinal anatomy:
http://en.wikipedia.org/wiki/Mediastinum

Typically the paraneoplastic symptoms precede diagnosis of the cancer.

I agree that paraneoplastic PN is not one of the more common types. You could forgo the CAT scan in the beginning because other tests may show something instead. Then you can decide later if you want to explore that possibility.