When I run a WinForms (or Delphi, see at the end) application on Windows 10 in a tablet mode, a touch keyboard does not pop up automatically, when an input box is focused.>
As far as I can tell, launching osk.exe or tabtip.exe pretty much is the "standard" way of making this work. I've found no "official" solution so far.
However, if it were me doing this, I wouldn't be killing the process or sending keys to try and dismiss the keyboard. Instead, you can obtain the window handle when you launch the process, and use that to minimize the window and hide it from the taskbar.
Someone here has gotten the window handle just to close it, but it gives you the idea: Show & hiding the Windows 8 on screen keyboard from WPF
If you need me to, let me know and I'll see if I can find the time to do up a full example.