No way that you can stabilize that thing on your lap.
However, a possible solution, is to affix an adjustable strap to the bottom of the unit.
Then tighten the strapping to your leg, to hold it in place. It still wont be 100% stable, but it will at least be
possible to use... IF you can manage to tighten the strap good enough.
Maybe add some rubber to the strap, to create even more friction, to help prevent it from sliding.
You might lose circulation in your leg... but I cant see any other way, to have something that small, being usable.
While I appreciate the fact that not everyone has a lot of additional space.. I dont understand how an additional
few inches can be a problem. I mean, you could make mounts for it under your desktop surface (upside down)
for example. Or hang it from the wall or ceiling?
There is another type of handheld joystick.. the "Epyx 500 XJ". I used to have it for my Commodore 64, and
it also worked with the Sega Master System. It actually uses a mini microswitch joystick. The buttons are on
the side.. and they were micros as well.
That stick only had two buttons, and IMO, is wasnt as easy to fire the buttons as a gamepad. But the sticks
accurate directions, made it possible for me to do a nearly impossible jump in Maze Hunter 3D for the
Sega Master System.
One might be able to modify that design, to have 4 smaller buttons, that are also easier to press.
Another spin on that type of controller, might be a vertical gun grip bottom, with 4 buttons in the
finger grip positions. The hard part might be in keeping from accidentally pressing the buttons,
while just gripping it.