I use 550 cord BECAUSE of the elasticity of it. I would rather have abuilt-in "fudge factor" than miss judge an application and end up going hungry. I have used 550 cord for snares successfully, I gut and use just the sleeve so the snare knot slips and grips easier. It works on rabbit sized game perfectly. I have used the inner cords for the smaller bird snares I set, but I have abandoned them because they rate of return is horrible. I did catch a woodpecker once but let him go unharmed (his heart rate may have been a little high ). I had built a natural fish trap that was starting to produce nicely so I was taking the bird snares down when I found him anyway.
I don't know the specifics of Dyneema but I would think that the shock load is less for the higher tensil strength and less stretch. A snared animal can put quite a shock load on a snare.
550 cord seems to work very well for my applications. If I need something stronger it is proly for a specialized application so I would bring the right rope/cord/cable/webbing anyway.