My experience of snares extends only to the rabbit and fox snares that can be bought here in shooting shops. But, both are just metal cable, the fox snare is steel and the rabbit one is brass.
Think of other things that cable can be used for, the brass stuff is often used for hanging pictures on the wall. There are plenty of modern interior designers that use fairly thin steel cable to suspend lights from ceilings. Fishing trace is a bit thin, but you might find some that wouls do the job.
How about things like piano wire? Or how about the kevlar/spectra superbraid fishing lines? The latter aren't stiff enough to hold a loop, but could be used where you can support them with twigs or grass.
Think what your line has to do, then think what there is around that might do that job, it doesn't have to come in a pack marked "Snare Wire". Just remember that indiginous people catch lots of small game with snares made of natural fibre cordage. Africans use bailing/fencing wire to catch antelope. Sure you can find something to use where you are.
Chris