Spiking Neural Networks (SNNs) provide an attractive framework for energy-efficient inference due to their event-driven computation and biologically inspired dynamics. However, efficient hardware realization of SNNs remains challenging because neuronal computations incur significant power and area costs, and uncontrolled approximate arithmetic can destabilize recurrent state updates when precision is not properly managed. To address these challenges, this paper presents ReSCom, a reconfigurable SNN accelerator that leverages stochastic computing to reduce hardware complexity while maintaining stable inference. The proposed architecture employs stochastic arithmetic for multiplication operations in neuron dynamics, while preserving exact fixed-point addition/subtraction operations. This stochastic strategy enables runtime trade-offs between accuracy, latency, and energy consumption. A unified reconfigurable neuron design supports Integrate-and-Fire (IF), Leaky Integrate-and-Fire (LIF), and Synaptic neuron models within a single hardware framework. Experimental results for MNIST inference on a Xilinx Artix-7 FPGA show that ReSCom achieves $92.80\%$ classification accuracy while consuming just $0.05~\mathrm{mJ}$ of operational energy per image at $100~\mathrm{MHz}$, outperforming the energy efficiency of recent state-of-the-art implementations. Furthermore, managing the stochastic bit-stream length allows explicit, dynamic control over accuracy-latency-energy trade-offs to meet target application constraints.