[HoneyBadger]

I've been thinking about this one. It might be possible-depending on how their bodies are put together-that Jotuns simply don't have the ability/dexterity to use a sling.

Throwing a spear is a little bit different-and requires a different set of motions from-using a sling. The whirling around required to hurl a stone from a sling might be something Jotuns just physically can't do. I've heard speculation along these lines about Neanderthals-that, because they were put together differently than humans in their shoulders, they were unable to use ranged weapons, and so humans were able to massacre them from a distance.
Jotuns-with their far heavier skelital structure, might suffer from the same handicap as Neanderthal-man.

In which case, the Jotuns could still use atlatls, grenade-weapons, harpoons with lines, "lawn-dart" type weapons, shurikens, and ofcourse crossbows. They also would probably not be able to use ball-and-chain weapons, but they'd be likely to use flails with several heads and various types of maces and nets, because of the area-effectiveness of those weapons-they're big enough that at times they could put themselves at a major disadvantage trying to use only precision-weapons, like axes and spears, against small enemies.