Dimuon production in neutrino-nucleus collisions, an important constraint of strangeness in global parton distribution function analyses, is typically calculated by assuming it to be proportional to inclusive charm production. This approach breaks down beyond fixed-flavor leading-order calculations. In our previous work, we introduced an alternative approach based on semi-inclusive charmed-hadron production to compute dimuon production directly. We now present an extension to this work, where we compute the semi-inclusive hadron production in the SACOT-$\chi$ general-mass variable-flavor number scheme to take all charm-mass effects consistently into account. The results are in line with our expectations, with the dynamical charm-mass effects modifying our previous approximative calculation by up to $20 \, \%$ at small values of $Q^2$.