You can set your monitor and TV to whatever priority you wish though W10 will only function as you mentioned as far as apps go. As for dragging it between the two, that's a bit of a gray area. Still, the resolution of the recorded source material is what will dictate if it plays correctly: playing 4k on 1080p is only going to display as 1080p; playing 1080p on 4K may be upconverted depending on what's playing the source or it may not. Blu-Ray players will either up or down convert based on the connected device's display ability. I can't speak to the software you'd be using and you'd need to look into the literature to be sure it converts.