Electrical wiring design within interior finishing is subject to various practical criteria, thereby resulting in time-intensive manual implementation. Despite this, most applications offer only basic collision detection tools, limiting design capabilities. In response, a graph-based decomposition approach is introduced, framing electrical wiring design as an optimization problem on a non-uniform grid graph derived from building information. This method breaks down the problem into two distinct subproblems, which are sequentially solved to achieve an optimal overall solution. Through experimentation across synthetic and real-world instances, performance improvements are demonstrated compared to two conventional integer programming solvers, yielding cost reductions averaging 12.3% when compared to a leading commercial application for interior design. These findings demonstrate the potential integration of this approach into building information modeling platforms, offering an efficient toolset for electrical wiring design in interior finishing.