Hi! :)
The C64 version of Space Cavern Blaster currently only supports standard one-button joysticks. I always thought it was not possible to use more, but your question made me search the internet again and you are right: there are methods to use 2-3 button joysticks/gamepads on a C64.
While two-button sticks are not the norm on a C64, i really like the idea and added two button support to my to-do list.
Thanks for the hint! :)
[Edit] For now, you have to press "Up" to jump in the C64 version.