For leather that has been on a spool a long time and is now curly, I
assume that the leather has dried out a bit and is therefore stiff.
You might try a leather conditioner like saddle soap or other product
made for saddles. I use Effax Leather Combi on my saddles and
bridles. Since it is a liquid, it would probably work better than
saddle soap in the application to a cord. Saddle soap is more like a
cream that must be rubbed in, where the Leather Combi is a thin
liquid that you apply then wipe off. It makes the leather soft,
supple, is grease free, does not change the color, and might just do
the trick for you.
Sun Country Gems