With the integration of wind power, photovoltaic power, gas turbine, and energy storage, the novel battery charging and swapping station (NBCSS) possesses significant operational flexibility, which can aid in the service restoration of distribution system (DS) during power outages caused by extreme events. This paper presents an integrated optimization model for DS restoration that considers NBCSS, repair crews, and network reconfigurations simultaneously. The objective of this model is to maximize the restored load while minimizing generation costs. To address the uncertainties associated with renewable energies, a two-stage stochastic optimization framework is employed. Additionally, copula theory is also applied to capture the correlation between the output of adjacent renewable energies. The conditional value-at-risk (CVaR) measure is further incorporated into the objective function to account for risk aversion. Subsequently, the proposed optimization model is transformed into a mixed-integer linear programming (MILP) problem. This transformation allows for tractable solutions using commercial solvers such as Gurobi. Finally, case studies are conducted on the modified IEEE 33-bus and 69-bus DSs. The results illustrate that the proposed method not only restores a greater load but also effectively mitigates uncertainty risks.