I believe the latest issue of Fly Rod & Reel magazine has a pretty good article about carry ons. I just glanced at it at the book store. Seems reels (with lines) are banned, as are any type hooks. The reel caught my eye, they said there was enough fly line and backing to tie up a whole flight crew.
And hooks are considered weapons. Can't you just imagine trying to attack a 200 lb person with a #24 dry fly? Anyway, you might want to check the book store and the article. It appears different airlines have different understandings.
Don't try to take your favorite knot tying tool with the clippers and hook eye cleaner point.