Yeah, cornstarch can work outside too, in my experience. I sprinkled some on my back deck stairs a while back, and it shut them up for a good part of the summer. But if your area gets a lot of rain, it might not last as long as indoor applications. The moisture seems to break it down or wash it out over time. So it's a decent temp fix, but you might need to reapply it now and then. Take that with a grain of salt, since all decks are built a bit different.
Referencing how it stopped the squeaks cold for both of you. @jordanp34, since your fix in the basement held up, does cornstarch work on outdoor deck stairs too, or just indoor ones like attics? I wonder if moisture messes with it.