  We compute the conformal blocks of the Virasoro minimal model or its W$_N$
extension with large central charge from Wilson line networks in a Chern-Simons
theory including loop corrections. In our previous work, we offered a
prescription to regularize divergences from loops attached to Wilson lines. In
this paper, we generalize our method with the prescription by dealing with more
general operators for $N=3$ and apply it to the identity W$_3$ block. We
further compute general light-light blocks and heavy-light correlators for
$N=2$ with the Wilson line method and compare the results with known ones
obtained using a different prescription. We briefly discuss general W$_3$
blocks.
