Design decisions made during high-level synthesis usually have great impacts on the later design stages. In this paper, We present a general framework, which plans for the clock skew scheduling in physical design stages during register binding in high-level synthesis. Our proposed technique pursues the optimality of the native objective functions of the register binding problem. At the same time, it ensures not invalidating the subsequent clock skew scheduling for optimizing the clock period. We use the switching power as the native objective of our register binding problem. The problem is first formulated as a MILP problem. An acceleration scheme based on the concept of weakly compatible edge set (WCES) is proposed to speed up the MILP solver to obtain the optimal solution. Then, we present our heuristic algorithm to reduce the running time further. The experimental results show that on average our acceleration scheme can speed up the solver by 8.6 times, and our heuristic is 70 times faster than the solver with a 5.25% degradation of the native objective. The minimum and maximum degradation among our benchmark set are 0.82% and 12.2% respectively.