By chance do you have a "Smart TV"? One that has internet (wired or Wi-Fi)?
If so, you might not need the HDMI cable. If you are running a Modern App, you can send video via the network by a charm swipe, select Devices, Play, and you might see your TV listed, if so, select it, and voil? wireless video on your TV!!
Oh, you do need the TV connected to your network, btw.