You aren't required to run a window manager at all. I've setup several such applications that are meant to be the only application ever run and they are meant to run full screen and I've never used a window manager. I always start with a server distro so a desktop and all of it's dependencies aren't loaded automatically. Then installed X and setup custom upstart/systemd scripts to start X at boot along with a custom .xinitrc. This sounds like it would fit your situation well. It takes a little know-how, but it makes for a lightweight system that's very portable.