How to connect external display to MacBook Pro without a cable?
I've used a few wireless dongles and other devices in the past and they've been hit and miss due to driver issues and other complications.

By far the easiest method is to use a AppleTV and use AirPlay to mirror or extend the display to the screen.

You would connect the AppleTV to the display using HDMI. After setting it all up you would then click the AirPlay icon in the upper right of your Mac's screen and select your AppleTV from the choices.

If your WiFi is nice and strong for both units, you should be good to go.