Not in Hawaii anymore. Alaska now. Much better for that sort of thing.
Snares hunt 24/7. You can take any game, even a moose (A good source is buckshotscamp.com). In true survival in Alaska (lived, hunted and fished there for 25 years) the moose population will be wiped out very quickly so hunting will not be productive. Squirrels? Snare or live trap. Not many rabbits. What are you going to shoot anyway? In any “grid down” in the NW, Alaska will not get food shipped. You better have a whole lot of food stored and hidden along with gear. Get a gill net sized for trout & dollies (In Anchorage: donalsoncompany.net). Slice open a porcupine and hang from a limb over water, the maggots will fall and attract fish. Put floats and weights on the gill net and run it out at night pulling it in before light. Gill nets also work through the ice with chumming.
A 177 break barrel pellet gun or 22 is also my recommendation, forget the slingshot, I have used them a lot and they are not accurate.
But,as you asked about slingshots and not air rifles, and are looking for something slightly more sophisticated...
http://www.pyramydair.com/s/m/Bone_Collector_Sport_Slingshot_Laser_Light/2839\ --Its also available on there without all the tactical doodads.
I recommend playing around with different rubbery materials and finding some cheap, easily accessable stuff to make your own bands with. Ammo too.