Untethered is not the correct word to use. 99.9% of domestic sheep in NZ are untethered.
A wild sheep will not have an earmark (notches of varying shape in the ear) or an eartag. Having a GPS and recording where you shot the sheep would be helpful in proving it was wild, but my understanding is if you kill a sheep (or any livestock) and it has an earmark or eartag, even if miles from the nearest farmland, you have to try and find the owner and give them the option of taking the carcass. If you cut the head off, make sure to leave the ears attached to the body, as proof it didn't have an earmark or eartag.
Wild sheep will normally have a lot of wool as they have never been shorn, but some domestic sheep may also have missed a shearing or two and have a lot of wool. If the wool is short it isn't wild, unless it is a young lamb or one of the shedding breeds.
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