None of Canon's cameras have built-in radio transmitters. The built-in wireless features are all dependent upon either:
- a pop-up optical flash
- a hot shoe mounted optical flash or controller
- a hot shoe mounted radio transmitter (including a hot shoe mounted flash that contains a radio transmitter, such as your YN600EX-RT)
Both optical and radio are considered "wireless."
Instead of using the 'Easy wireless flash' option, you may need to try the 'Custom wireless flash' option to access a menu option that tells the pop-up flash to only fire the pre-flashes needed to control the off camera flash, but to not fire when the shutter is open. I've not used a 77D, but most older x0D models released since 2009 will allow the built-in flash to be used as a controller without firing again when the shutter is open.
There is another simple solution to your delima if you don't need to move the flash very far off-camera: an off shoe cord.
They come in lengths from 1.5' to 10'. They are a very economical option for getting the flash off camera while still retaining TTL capability. This one (pictured above) costs about $20 at amazon. The official Canon version is about $70. There are some really cheap ones currently available for not much more than $5.
From the OPs comments to another answer:
I can use it as an optical slave, but it won't be ETTL.
The YN600EX-RT II is capable of being used both as an optical master and as an optical slave. Your 77D's pop-up flash should be capable of controlling the YN600EX-RT II optically in TTL mode. You should also be able to set the pop-up flash to only fire as a controller, and not fire after the shutter opens.
If the pop-up flash and the external flash do not seem to be communicating, be sure you have the YN600EX-RT II set to 'Group A' (assuming your camera is set to the default setting). Also confirm that 'Group A' is enabled in the camera's menu.
I might buy a YN-E3-RT transmitter, BUT (sigh) will it trigger 2 of these flashes?
Yes. The YN-E3-RT and YN-E3-RT II can control up to 15 flashes in 5 groups.