Supposing it is solid and wouldn't snap or break. Would it guillotine you or just pass through leaving you unwounded?
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No, you would still be much the same you were before the event.
The bonds of the molecules that make your body would quickly reform. The wire would need to be of a size compare to molecules, rather than atoms, to possibly cause tissue and bone damage damage. Even then, your body would still survive.
The only serious injury I can think of is to your nerve cells, so a wire passing through your brain or spinal cord may be a problem.
Single atom wires are not yet available, so I can only give you my opinion, but graphene sheets on the same scale are discussed at Science: Graphene Sheets and the strength of these is covered by this article.