My experience has been with Apple TV and an HDMI cord that I bring. I bring and store these for each visit in my Owner's Locker. There are two methods to connect HDMI devices from the device to the TV:
1) (may have issues) using the open HDMI ports on the back of the TV
2) (preferred) connect to the empty HDMI input on a black box/controller typically mounted to the wall behind the tv. This black box seems to be the controller for the hotel-based services and often has an open input.
In my experience, by using the open HDMI input on the black box, the television remote control can be used to control the volume, and you don’t have to adjust/move/remove any of the existing cables (which I would not recommend anyway).
Once your HDMI-based device is connected and to select the input for method #2, you do have to access the settings menu using on the television remote control provided by Disney to select the alternate HDMI input. I am not currently at the resort, so this description may not be the exact the process, but once you select the alternative input, the input and television volume should work with that HDMI port. I had issues using method #1 with controlling the volume.
I’ll be back at the resorts in a few weeks and will try to refine this description.