The voltage-gated ion channels embedded in biological membranes play crucial roles on the generation and transmission of action potentials. Therefore, understanding of impacts of each ion channel is of great importance for the dynamics of neuronal networks. Among the others, one method on this way is to block a specific ion channel type while keeping the remaining ion channel types active across the membrane and to observe their impact on neuronal dynamics. In this study, we study the effects of sodium and potassium channels blockage on the collective spiking regularity of a scale-free neuronal network with stochastic Hodgkin-Huxley neurons, and investigate how the dependence of the collective spiking regularity on the membrane area or cell size varies with the coupling constant between neurons. Results reveal that the collective spiking regularity exhibits coherence resonance (CR) depending on the channel blockage scaling factor and the cell size, where potassium channel blockage enhances the collective spiking regularity whereas sodium channel blockage decreases it. We show that there is a lower limit for the coupling constant which warrants the CR behavior. We also show that the maximal regularity is obtained for a smaller cell size with the increasing the value of the coupling constant.