Here is an earlier effort of Sierpiński: *Sur une propriété de la décomposition de M. Vitali*, [Mathematica 3, 30-32 (1930)][1].
He took "Vitali's Decomposition", that is, the family of cosets of $\mathbb{Q}$ in $\mathbb{R}$ and divided it into (unordered!) pairs $\{Q,-Q\}$ of symmetric sets (thus excluding the one symmetric coset: $\mathbb{Q}$ itself).
Given a choice set $\mathcal{Q}$ for this family of pairs let $S=\bigcup\mathcal{Q}$. Then $S$ is non-measurable. 

Thus you can get a non-measurable set from AC for pairs, or from the existence of a linear order on the power set of $\mathbb{R}$. He already mentioned the latter in 1917: *Sur quelques problèmes qui impliquent non mesurables*, [C. R. 164, 882-884 (1917)][2].


  [1]: https://zbmath.org/56.0921.03
  [2]: http://gallica.bnf.fr/ark:/12148/bpt6k31178.f882