I might try bending them into a loose knot, and then clamping the end in a vice, and tightening the knot into a ball size by heaving on the other end. Might not work.

Or you you thread a small bead on to the string, and work out how to stop it coming off the end. Solder might do the trick.

But the sites I've used to buy strings from do seem to say whether the strings are loop or ball. Try looking around more sites.