Due to the inherent uncertainty of wind conditions as well as the price unpredictability in the competitive electricity market, wind power producers are exposed to the risk of concurrent fluctuations in both price and volume. Therefore, it is imperative to develop strategies to effectively stabilize their revenues, or cash flows, when trading wind power output in the electricity market. In light of this context, we present a novel endeavor to construct multivariate derivatives for mitigating the risk of fluctuating cash flows that are associated with trading wind power generation in electricity markets. Our approach involves leveraging nonparametric techniques to identify optimal payoff structures or compute the positions of derivatives with fine granularity, utilizing multiple underlying indexes including spot electricity price, area-wide wind power production index, and local wind conditions. These derivatives, referred to as mixed derivatives, offer advantages in terms of hedge effectiveness and contracting efficiency. Notably, we develop a methodology to enhance the hedge effects by modeling multivariate functions of wind speed and wind direction, incorporating periodicity constraints on wind direction via tensor product spline functions. By conducting an empirical analysis using data from Japan, we elucidate the extent to which the hedge effectiveness is improved by constructing mixed derivatives from various perspectives. Furthermore, we compare the hedge performance between high-granular (hourly) and low-granular (daily) formulations, revealing the advantages of utilizing a high-granular hedging approach.