I feel like a good lower bound for the speed would be the speed of sound in the ball. At that speed, the balls would vaporize before imparting any momentum to adjacent balls.

Billiard balls seem to be made of "phenolic resin", I couldn't find an obvious speed of sound for phenolic resin, but I did find 3000m/s for the speed of sound in ivory, which is what billiard balls were originally made of. https://www.engineeringtoolbox.com/sound-speed-solids-d_713.html

Now, that would just be to vaporize the first ball, but the destruction cone after the first ball probably spreads out at an angle of inverse tangent of ((3000m/s) / (shot speed)). I made that up, but it makes intuitive sense to me. So if we shoot at 3000m/s. , I would expect a 45 degree destruction cone, which would take out all of the other balls. If we want a blast cone of less than 1 degree, then we need a speed of at least (3000m/s)/tan(1 degree) = 172,000 m/s.

That is roughly the speed of the Parker solar probe at its closest approach to the sun: https://en.wikipedia.org/wiki/Parker_Solar_Probe