I would like to have a windowless OpenGL context (on both GNU/linux with Xorg and Windows). I\'m not going to render anything but only call functions like glGetString<
glGetString<
You need a window to host the context and you need a context to be able to do anything.
Source
If you don't want to display anything make the window invisible.
If there was another way to do this, it would be documented somewhere and easily found as it's not an uncommon problem.