A cylindrical magnetic nanowire system composed of ferromagnetic core and shell layers has been investigated by using effective field theory (EFT) with correlations. Both ferromagnetic and antiferromagnetic exchange couplings at the core–shell interface have been considered. Main attention has been focused on the effects of the quenched disordered shell bonds, as well as interface bonds on the magnetic properties of the system. A complete picture of the phase diagrams and magnetization profiles has been represented. It has been shown that for the antiferromagnetic nanowire system, the magnetization curves can be classified according to Néel theory of ferrimagnetism and it has been found that under certain conditions, the magnetization profiles may exhibit Q-type, P-type, N-type, and L-type behaviors. The observed L-type behavior has not been reported in the literature before for the equilibrium properties of nanoscaled magnets. As another interesting feature of the system, it has been found that a compensation point can be induced by a bond dilution process in the surface.