The correct reference is 

 - Olaf Neumann, <em>Two proofs of the Kronecker-Weber theorem "according to Kronecker, and Weber"</em>, J. Reine Angew. Math. 323 (1981), 105-126 

This is also the source that Schappacher relies on. Neumann analyses Weber's first proofs
(there's not much of a proof in Kronecker) and points out his errors (he overlooked that
the Galois group does not always act nicely on Lagrange resolvents if the fields in question
have a nonempty intersection). Weber's proofs, strictly speaking, were only fixed by Neumann; 
the proofs in between did not use Lagrange resolvents, except for a proof by Mertens which
suffers from the same defects as Wenber's.