I would in no way ever encourage somebody going out on a long trail with no food but if you do I would suggest fishing rather than hunting, for one you don't have to worry about gun laws, 2 most trout fishing in any state is legal during the hiking seasons.3 if you mess up while using a fishing rod you won't kill somebody or yourself. I know Washington has many mountain lakes with eager trout I could point you toward some and give you advice. If you do this bring at least 3 days of food and save it as an emergency supply in case you realize you have to go back to civilization so you don't die along the way.

Other notes, as far as I know fishing in all national forest/parks does not require a state permit. Also fishing gear is way lighter than a gun and ammo is. I would try fishing in the lakes you plan to hit before you decide this some lakes can't support fish population naturally and just cause you find information it was stocked 4 years ago does not mean fish still live in it. Best of luck and pm me if you have any additional questions