How long can Alaskan king crab live out of water?
Depends upon if it gets caught or eaten.... :) "Life Span of Snow Crab Alaskan Snow Crab are long-lived compared to warm-water crab, like Dungeness Crab. They may not reach adulthood until 6 or 7 years of age and may live more than 10 years" from: http://www.crab-o-licious.com/alaskan-snow-crab.html
There is at least one supplier that advertises shipping King Crab legs as fresh cooked - never frozen. They overnight the package and are available that way for a limited time. I imagine the package has chill packs or dry ice to keep it cold. You could get raw King Crab legs only if you live in a crabbing community.