A couple of tutorials to make your own swift have been linked here and on Craftster if the prices are making you back off. I made my own and it was fine.
I have also wound on my ball winder while holding the hank myself: I wind with one hand. With the other I hold the hank at one point, it hangs down toward the floor. I don't wrap my fingers around the wool - it justs hangs off my hand, back of hand to the floor, palm toward ceiling, hand fairly flat and open. When the wool from the portion of the hank on my hand is peeling away from the hank toward the ball winder, I slow down if necessary, and I move my hand slightly so that the wool can peel away easily. After doing this you may find the ball is too loose, and you may want to rewind it (from the centre). Not too tight either!
If your ball winder is to rewind balls so they are uniform and stackable, then you don't need a swift, but if you plan to wind balls from hanks, you can use a swift.
You may like to block your pieces first, this may lessen the curling slightly, and make it easier to assemble (depending on the fibre content).
BTW, a question for the Yanks: is a skein a ball, or is it a hank?