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There is basically NO air at 100,000 feet or above.

The air pressure at sea level is about 14.7 psi (or barometric pressure is 29.92” Hg)

The air pressure at 25,000 ft is about 5.5 psi (11.12” Hg). Almost 2/3rds lower.

At 50,000 ft - - 1.7 psi (3.44” Hg).
At 75,000 ft - - 0.5 psi (1.00” Hg)
At 100,000 ft — 0.16 psi (0.33” Hg)

At 100,000 feet your are in a strong vacuum - only 1.1% of the air remains - 98.9% less air means MUCH less air friction / drag.

That is why they MIGHT be able to break the speed of sound in freefall - there is almost NO force exerted by the air as drag. He will fall and continually accelerate, almost completely unhindered by drag.

(Thus aerodynamics isn’t really a factor. If one WERE to drop a P-51 from 120,000’ (with it’s prop featherd and engine NOT running) I can almost guarantee it would break the local speed of sound. I cannot guarantee it would make the transition to denser air as it falls without shedding its wings.)

As the air pressure increase, drag will increase and his speed will slow naturally.

I am not sure at what altitude and speed he will reach maximum dynamic force (product of increasing drag and decreasing speed).

The extra altitude he starts at WILL give him a better chance of reaching a terminal velocity that IS faster than the speed of sound at that altitude.

One possibly BIG issue with breaking the sound barrier will be if some dynamic factor caused by fluid dynamics of the air around him causes some sort of flutter (high-speed vortex shedding from his hands for example).

If something like that occurs, he might experience tremendous force variations and be seriously injured.

BUT that is normally more a problem with rigid structures. The body being soft / compliant, I think this is unlikely.

For HIS sake I hope it is unlikely...

He will not be "unhindered" by drag, because this is not merely a function of air density but also velocity. The 1.1% of air will have a drag effect that will oppose gravity linearly (if there are no shock wave effects which will only slow him down even more) as his speed increases. Even at 150,000 meters there is sufficient drag to slow down low earth-orbit satellites -- although they are moving 30x faster than the speed of sound.

The big problem even a small amount of drag can cause him is rotation. As soon as there is enough air to have even "negligible" effects on his radial velocity, he will start to turn, and he will spin very quickly without stabilizers.

Ignoring air resistance completely, the best case calculation says he can hit the local speed of sound (around 300 m/s) when he gets slightly over 116,000 feet. I think 120,000 is more like what he needs, but even there I'm not sure it's quite high enough.

I don't work in the field any longer, but most of my research was done at 10^-6 - 10^-9 atmosphere, so I laughed at 10^-2 as a "strong vacuum." I suppose in some applications it is. "Strong Vacuum" is not a term-of-art in my old field (low energy physics.)