Although 網球與羽毛 look similar, their techniques are quite different. 羽毛's footwork consists of smaller step than of 網球. 羽毛's hit motion relies more on wrist snap; while in 網球, you lock the wrist and generate power from your body's rotation and arm follow through to generate racquet speed.
You can lean both at the same time but leave the other sport's technique at the door before stepping onto the court. Otherwise, you will be messing up you game and worst get injury.
Last, you can wear tennis shoe or cross train shoes for tennis; but never running shoe if you are serious about game. Running shoes do not have the side-to-side and backward supports that tennis shoes offer.