Higher-order hadronic corrections to the anomalous magnetic moment of the muon have been evaluated including next-to-next-to-leading-order insertions of hadronic vacuum polarization and next-to-leading-order corrections to hadronic light-by-light scattering. This leaves a set of mixed leptonic and hadronic corrections in the form of double-bubble topologies as the only remaining hadronic effect at O(α^{4}). Here, we estimate these contributions by analyzing the respective cuts of the diagrams, suggesting that the impact is limited to ≲1×10^{-11} and thus negligible at the level of the final precision of the Fermilab g-2 experiment.