I just returned from a flight (with connection) to CO and was thinking about a 'minimalist kit' that would be permitted within carry on luggage. So your question is very similar. Speaking solely about tools, here's what I came up with: 1)Scissors (legal for air travel although I have to find out); 2)Bobbin; 3)Hackle Pliers; 4)Head of a Toothbrush with the bristles cut down; and, 5)Hair Stacker. That's it.
I can get by without a half hitch, a whip finisher, bobbin threader, dubbing needle and other misc. tools.
Allan
PS - I just looked it up and here's what I found out about scissors: "Scissors: metal with pointed tips and blades shorter than four inches" are allowed on a flight." So I guess my tying scissor that is 3-1/2 inches is okay.