They do not run locally at this time.
If you set them up with a direct connection to a Zigbee Device in the same room, which I believe some people have done, then that would be local. But I also know some people were having problems doing that.
But the DTH definitely does not run locally.
And, no, you can’t just randomly change to some other DTH. Think of a DTH like a printer driver. Its whole purpose in life is to Create a message in the exact format that that specific device is expecting to receive. If you’re just talking about a basic function, like an on/off switch, then you might be able to change to a different driver. But any of these multi button devices have quite complex functionality and unlikely to be able to work with a different DTH. Even different firmware on the same model may require a different DTH.
Talk to the people in the following thread: