Although they are edible, green crabs aren't often actively pursued by crabbers. Also, they don't get very big, only to 3-4". Green crabs in Puget Sound spells trouble for other species of crab such as Dungeness. And actually I believe that the WDFW is doing a survey of green crab distribution, so if you catch one, take note of where you caught it, time of day, rain or shine, it's size, sex, water depth, number caught and so forth.
Personally I'd also rip their claws off and throw them back into the water so as to make them easy prey for large predators. And if you're inclined to kill them, more power to ya!