How thin can an indestructibly sharp wire be for it to pass through your neck extremely completely and extremely quickly without killing you?

For example, if I were to drop a 1mm thick guillotine through your neck at 1000m/s, passing completely through your neck, you would not survive. What if it were 0.1mm thick? Or if were 0.01mm thick?

How thin would it have to be for it to pass through your neck extremely quickly for you to survive it? Does the speed of which it passes through your neck matter?