you got a pic so I can see exactly. But if i'm thinking correctly, the switches that is use in the joysticks has a METAL arm connected to it.
But if you at both switches (Buttons and the Joysticks), it is exactly the same except for the ARm piece. If so, I have done something like this. Break off the METAL ARM and place in one of your Button Switches. The BAD switch, just rip off the plastic piece thats holding the ARM and when you place this ARM in your NEW cherry switch, place it in carefully. You can actually widen the cherry switch just a touch tho. If you have too, with exacto knife, thin it out a bit or make a slit so you can just slip the ARM in then use BONDO or METAL/BONDO to cover the slit, but most likely during gameplay, the ARM will not fall off anyway, the switch is lying on its sides.
Hope that make sense...