first check - surreptitiously - that is is actually illegal.
I can't imagine it would be.
In which case legislation is not necessary.
That fact that you will most probably leave a trail of badly injured animals behind you - is on your own conscience.
Bear in mind how far an injured animal can run even when shot through the heart.
Unless you are using some sort of bolas ammo - and that's probably all I would consider hunting with. Then whatever you hit will likely run, climb, go down it's burrow before you get close enough to dispatch it cleanly.
I'm not against hunting - just against cruelty to animals.
If you intend to kill something - do it cleanly and quickly - I honestly don't feel a sling is suitable for that.
But like i say, your call not mine. I would bet no legislation exists. Also you'll be hunting on your own or your neighbours land. So it's not like any officials will ever see you.
I find that it really doesn't pay to give local officials ideas. It makes their brains hurt
If you don't ask them - they'll probably never consider it, ever.
Unless you start a sling hunting club and advertise in your local paper.
I figure you're brighter than that