As part of the existence of the Hilbert class field, we have the following equivalence :

Let $ k$ be a number field. Then the class group of $ k$ is non trivial if and only if $ k$ has an abelian extension which is unramified everywhere.

How much of that needs advanced Class Field Theory ? More precisely : – is there an easier proof of the fact that if $ \mathcal{O}_k$ has a nonprincipal ideal, then $ k$ has a nontrivial extension which is unramified everywhere (even just proving this at finite places) ? – is there an easier way of finding a nonprincipal ideal of $ \mathcal{O}_K$ starting from an unramified abelian extension ?

The second question is actually more or less answered as Satz 94 in Hilbert’s Zahlbericht. Is there a transparent modern way to see it ? Does that mean that the first question is the hard one and needs all the CFT machinery ?