Not feasible. That would entail putting shrapnel into orbit (unlike extant anti-sat weapons which are short-range suborbital), which would mean a full orbital launch for every satellite target orbit. There's hundreds[0] of Starlink orbital groups already, so that'd require hundreds of independent orbital launches in a short timescale—far beyond China's launch capabilities today.

[0] https://planet4589.org/space/con/star/planes.html

(On general principles, you could argue you'd need 1:1 launch vehicle parity (number, not payload) to defeat a satellite constellation this way. For each satellite launch, you'd need one corresponding anti-satellite launch into that same, newly-defined orbit).

For your shrapnel to hit the satellite, it needs to be at the same height and inclination. Otherwise, your shrapnel will likely miss the targets.

Starlink satellites are pretty low and experience a lot of drag, with square-cube law working against you. Your shrapnel's orbit will likely decay pretty rapidly.

Tiny propellant burns turn into thousands of kilometer changes quickly.