40" is very short and with a nonbinding handle its even worse, you are probably looking at a 15" draw length, for now paracord won't be that bad but you should look into getting something else, modern materials include b-50, fastflight,D97, artificial sinew, the list goes on. More historical materials linen, rawhide,sinew,flax, animal gut, silk, nettle, milkweed,dogbane, and more.