I would go with a disposable flosscard arrangement--making it reloadable would only increase thickness. If you cut open a floss card, you see that they are not tightly packed. If I remember correctly, the floss is laid down very loosely in a back-and-forth manner on a light, double-sided adhesive sheet. Then the other side of the adhesive is attached to one of the two layers of plastic of the card. If you’ve carried a flosscard in a wallet, you will have noticed that one side (its thinner) of the card does not wear as well. I can envision having two different sizes of cordage in one card—something light like floss from one end and a heavier cord (maybe 200# Spectra) from the other. Whether one or two types of cord are used in a card, they could be packed much tighter than the floss in flosscards (at a cost).
As to needles: Are they banned yet? I keep some fishing hooks, sewing needles, and T-pins taped to the floss card in my wallet.
As to scissors: Martin Focazio has at least twice mentioned that he carries paramedic shears on flights—the type that can slide under a bandage without scratching the skin. These are considered blunt nosed shears. Some are advertised as being able to cut a penny in half. They could easily cut a seat belt. If you have not looked at these as a tool you can take on a flight, do so. The ones sold at the local drug store (for way to much money) did not have contoured finger and thumb holes-- probably some type of medical supply house would be the best place to purchase them. I have been considering getting just the shears from a Swiss Army Card to put in a small FAK; but I’m not sure if they would be considered too pointed.