A theoretical approach to investigate the influence of CO and H adsorption on the compositional structure or chemical ordering of binary metal nanoclusters is applied to selected representative pairs: AuPd, PdPt, CuPt and PdRh. The truncated octahedral (TO) 38-atom cluster is chosen as a model of small fcc nanoclusters because its high-symmetry allows a simpler analysis and a reduced computational effort. A number of CO and H ligands (ranging from 1 to 8) are adsorbed on atop sites at the centre of (111) facets of the cluster, and the corresponding energetics are analyzed in detail. A strong tendency to segregation inversion from AuPd shell/core to core/shell is found upon CO adsorption, qualitatively very similar even though more pronounced than that found for the PdRh pair (where Pd plays the role of Au and Rh that of Pd). This effect is still present, but quantitatively modest, in PdPt. The value of the CO binding energy decreases in the sequence: Rh > Pt > Pd > Au, and is scarcely affected by the presence of neighbouring hetero-species (minor electronic effect). A clear electronic effect is instead found in the CuPt case, in which the strengthening of Pt-CO bonds when Cu neighbours surround the interacting Pt atom brings Cu from the centres to the edges of (111) facets in Pt-rich clusters upon CO adsorption. H adsorption brings about qualitatively similar effects, although to a much smaller degree, so that a definite segregation inversion is only predicted for the AuPd pair. The predicted trends are found to be in good agreement with available experimental results.