At 20,000 RPM, I'd say BELT.
Less stored energy when the chain breaks.

For this you want the smallest pulleys possible to keep the linear
speed down- less stored energy.

20Krpm, 1 inch diameter pulley, the belt's moving at, lets see...

dist at edge = radius times theta, theta is 2pi, 2 x 0.5 xpi = pi
inches per rotation. 20,000 pi is 62831.
So 62.832e3 inches per minute, or 87.3 ft/s or just about 60 mph (which
is 88ft/s).

Not sure a belt will survive turning a tight radius at these speeds.

Maybe a housing with a shaft drive and bevel gears might be found?
You could come straight off the die grinder and just do 1 90-turn at
the head.

Dave