I decided to play around with the Skype Win10 App [version 12.1815.210.0] this morning and, on the whole, it seems (to me - big proviso there) to be accessible.
I can land on all major controls, most have keyboard shortcuts, and I'm getting back and forth content in a single text messaging thread read back by NVDA.
If anyone wants to play around with Skype in the Win10 App version to try to figure things out let me know. In combination with Quick Assist to let me see what's happening on the other end it's likely that the interface can be figured out, as I've seen much, much worse in terms of access to controls, lack of labels for same, etc.
Brian - Windows 10 Home, 64-Bit, Version 1803, Build 17134
A little kindness from person to person is better than a vast love for all humankind.
~ Richard Dehmel