I don’t think you have to manually set 4K resolution in Special K.
For me, I only have to set 4K resolution and Windowed Mode in Tales of Vesperia settings.
Then, in Special K settings, under “Window Management” > “Style and Position”, just check “ Borderless” and “
Fullscreen (Borderless Upscale)”
(In ini file, it’s “Borderless=true” and “Fullscreen=true”).
And the game will always start in fullscreen.