There are all sorts of stainless steel wires, straightened, anealed and on and on. The best I have found for snares is .015 inch aircraft safety wire. It is the exact same wire packed in parachute harness survival kits for C-9 emergency chutes, and in other US military survival kits. It is about 30 to 40 Lb test for folks that worry about that. More than strong enough to snare small game. It also can be formed easily with just your fingers, no tools needed. It is hard to cut without a good cutter though! Do a web search for .015 stainless steel safety wire, usually about $10 per pound. A pound is a lot of snare wire!! CHeers!
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No, I am not Bear Grylls, but I stayed at a Holiday Inn Express last night and Bear was there too!