Scott and I are both aviation mechanics. Safety wire is not meant to keep a bolt or nut torqued. It's there to stop the un-torqued bolt or nut from completely backing off of the fixture it's meant to fasten, and departing the fixture. It's there to prevent a spinner that has become un-torqued from completely spinning off the hub. As stated, the torsional momentum of the wheel should keep the spinner torqued.....but weird things happen.
Stainless safety wire will stretch and break easily. Don't rely on it to keep it torqued.
The pigtail is simply to keep from poking stainless through your fingers.
As Scott said, the smart way would be to wire from the wheel to the inside of the spinner. This will prevent road debris from breaking the wire, and conceal it better. However, the authentic wire was at the tip. Functionally, it makes little difference.
If I was racing with wheel changes during the race, I'd put a clip on the end of the safety wire to clip into a hole in the spinner tip, after torquing. When racing motorcycles, we often did this with things like the oil drain bolt, axle bolts, etc. It made for a quick swap while still having the safety wire function. So, the safety wire would be loose with a clip on the end, clipped into the fixture.
The point being, this is about authentic aesthetics. As long as the safety wire is not broken it will do its job.