There are some good videos showing men using several kinds of slings. I believe that David used.the variation that has the cord connected to a stick/staff. It provides more power than even the regular sling. Goliath commented on David's "staves", plural.
It would have been more than a cumbersome handful to hold two staves/ sticks/ clubs/ blunt trauma impact weapons in one hand while swinging a standard cord sling. It makes more sense to me that there was one weapon in each hand.
The most recent one is called the Balearic or Staff Sling. There are different ways to throw with it. It was discovered in the late Roman period, however it doubtless existed previously. I've seen demos on how powerful one can be against a sheet of plywood. The archeological history shows that they were used in warfare.
Balearic Sling