Given how huge apps are, I figured there might be something in Apple's App Store. And lo and behold there is "an app for that." It's called Fingering Woodwinds for iPhone ($4.99, iTunes link). The developer does have a separate iPad version as well for $6.99. While I would like to review that one as well, sadly at the time of writing I don't own an iPad.
Fingering Woodwinds for iPhone is a great app. It's not perfect, but every woodwind artist and band director (or someone who deals with multiple instruments) should spend the $5, well worth it in my opinion. In fact, for the band directors who need quick access to both brass and woodwind fingerings, Patrick Q. Kelly has an app for that too.