It does not sound like you want to use a full-blown Ubuntu with the Unity desktop environment for this. Generally speaking, there are many window managers that allow more precise control of input.
In case you are new to Linux and graphical environments: There are three aspects of how linux renders nice, high-resolution output - the X-Server, responsible for hardware interaction, the window manager (metacity in the case of unity), which offers ... well, the ability to manage windows (i.e. close programs, move windows, etc.) and, finally (and optionally) the Desktop Environment. This is what adds all the fancy buttons, taskbars, the clock, etc.
If you only want one window to run, you should probably look into more cut-down graphical solutions, especially because your use-case does not require a full-blown Desktop Environment in the first place.
This StackExchange article offers some further recommendations. You could, e.g. look into the program Sabayon, or, which may be more fitting, use the linux distribution Fedora, which offers a specific kiosk variant.