The proof that $AC$ is independent of $\sf ZF$ axioms is done by forcing, and this doesn't beg any consistency strength more than that of $\sf ZF$.

Is there a known similar proof of independence of $AC$ from $\sf Z$ that is done at the consistency level of $\sf Z$ itself?

More generally what is the smallest consistency level we need to prove that $AC$ is independent from axioms of $\sf Z$?