What was the fastest recorded flight by a man without an aircraft?

Technically there has yet to be a flight without an aircraft by man, unless you count the stories of Icarus.

Flight is the ability to produce lift, and travel a given distance through the earth's atmosphere. For the average man, flapping his arm simply does not work. Parachute jumps are not flight because all the time you would be falling, not flying. So you need some form of vehicle or "aircraft". Most versions are powered, such as Planes, Helicopters, Rockets, Microlights etc etc etc

If you don't want to go via the powered flight route, then you'll need something like a balloon, or hang glider. Make no mistake though these are all still forms of aircraft.

The average speed for a tethered space walk is 7.7 km/s or 17,244.41 mph.