Bows/crossbows should be restricted to use in special clubs, just like guns or rifles, where they are stored on premise.
Restricting slingshots would be hard to enforce, but I'd say carrying them in public should be just as illegal as carrying guns.
Tbh I've never seen a use case that requires ownership of a slingshot, other than maybe feeding fishes in preparation of a long cast.
Should be reserved to professional hunters/game keepers, who would be entitled to rifle ownership as part of their job description, just like police forces or the military.
Privateers should not kill animals for sport.