Doesn't help the cause if you're already doing a long-distance flight...

Passive mm-wave scanners do not produce radiation. The active mm-wave scanners use non-ionizing radiation which has been studied and shown not to cause cancer. One study even suggested it might reduce metastasis:

http://onlinelibrary.wiley.com/doi/10.1002/bem.20208/abstrac...

The flight itself isn't even that bad, but it is worse than the scanners. You get maybe 5 mrem (50 µSv) flying from London to NYC.

http://hps.org/publicinformation/ate/faqs/commercialflights....

The flight radiation is something you'd want to avoid, but a single flight is almost insignificant. XKCD has a reference chart:

http://xkcd.com/radiation/

Flight radiation is mostly a concern for flight crew.