Altermagnets acquire a momentum-dependent spin splitting without net magnetization or spin-orbit coupling. This raises the question of whether the transport anisotropy originates in the electrons or the magnons, and whether the magnon-mediated channel distinguishes an altermagnet from a conventional antiferromagnet. We compute the spin-resolved conductivity of a metallic ferromagnet, antiferromagnet, and altermagnet within a common model, treating the spin-diagonal channel with the magnon self-energy and the spin-flip channel to leading order in the electron-magnon coupling. The anisotropy of the charge-spin conversion is dominated by the electronic spin splitting, the magnon branches contributing only marginally. The magnon-mediated spin-flip channel is even under C₄, so it carries no signature at first order in the anisotropy and cannot on its own distinguish an altermagnet from a conventional antiferromagnet. It does, however, respond linearly to a sublattice-selective perturbation that lowers the bulk B_1g symmetry. The resulting susceptibility vanishes identically in the antiferromagnet, is small in the ferromagnet, and is finite in the altermagnet, where the electronic anisotropy ties spin and sublattice together, so that among magnets with no net magnetization it is unique to altermagnetic order. Being even in the magnetic domain index, this response can be measured without preparing a single magnetic-domain sample.