This paper investigates the computational cost of modeling the response of the Type-I and Type-II cutaneous human mechanoreceptors for neuromorphic texture classification. We examined both the number of floating operations for modeling the receptors, and the number of synaptic operations for recurrent spiking neural networks (RSNNs) used in classification. Results show that deeper receptors (Type-II) require a greater computational cost to be modeled than those close to the surface (Type-I). However, RSNNs linked with deeper receptors exhibit a lower cost. We evaluated the energy consumption of the modeling and classification parts, each on its dedicated hardware device. The results suggest that pairing Type-I receptors with their corresponding RSNNs offers the best trade-off between energy consumption and classification accuracy.