Hi! Welcome to the jam!
The mouse movement is not accepted, it's more or less 4 buttons in itself (up, right, down, left).
I'm sure you'll find something with actual buttons :D
Btw, it's allowed (and even advisable) to offer alternatives for a function.
For example, if you have X to jump and C to shoot,
you can also have Mouse button 1 to jump and Mouse button 2 to shoot. That still counts as 2 buttons.
You can also keep ESC to quit the game, but it would be nice to be able to navigate the menus and quit the game with the 2 buttons too.
Have fun! =)