I would like to chime in here. About fifteen years extensive SAR experience operating in Arizona mountains, deserts, and caves. I always carried a minimal cookset in my pack - Trangia alcohol stove and aluminum cookset almost always, grading up to a liquid fueled stove for winter conditions. I always liked the alcohol setup for absolute ease and dependability of operation. I could start the stove, begin boiling water, and then attend to the victim or some other critical task. With the medical and technical climbing gear we carried, light weight was a definite consideration.
I noticed in another post that you stated you were issued MREs. They do have their place, but I much preferred my own cuisine - typical lightweight backpacker's fare, adjusted for my own taste. The total weight was much less than MREs.
I can't imagine a realistic combination of SAR and foraging - tracking game when your primary mission is tracking the victim? I can recall times when we passed up the opportunity to scarf up berries or go fishing in order to deal with the business at hand. If I did have to eat a squirrel or fish, I would simply put them on a spit or throw them on the coals - no gear needed.
Gear for personal use probably should vary somewhat from the dead simple requirements for SAR. In any event, the stainless steel is simply needlessly heavy. I would go with either coated aluminum or titanium - either material will last forever.