Understand that this is just 'armchair quarterbacking' as I have never been is such a situation, but IMHO if you are concerned about critters in the woods for which you would want to pack a .44 then I would tend to lean toward a DA capable unit (my Colt Python does both SA/DA).
My reasoning is that a critter large enough to want a .44 will generally have a mass and/or speed advantage over you (bear, cougar, elk, etc....even the two legged kind). Critters generally don't give you time to think about your response (Read: thumb back that hammer for each shot). This means you stand a very good chance of being in a situation where you're hopped up on adrenaline, and you just want to make the durn thing go BANG as many times as possible, as quickly as possible, while keeping it on target. (though I suppose you could practice 'fanning a SA).