Hmmm, as the A & B buttons are GENERALLY more necessary for everything and will timeout after a while(idk about the V2 I have one incoming, but it might be necessary for the minigames) you MIGHT be able to temporarily fix it by opening it up, and cutting the button rubber bits (cut off as little as possible, that flat bit by the board helps stabilize everything) and essentially putting the C button where the B button goes. That ought to do the trick at least until you find replacement buttons if you want to try running it right away. Just know that it'll make it so you can't cancel out of a menu, go backwards when setting your birthday or time if you make a mistake when setting them(although time is easy enough to change later), and it might make a few minigames unplayable in the meantime(although as it is now, it'd be rather cumbersome to play. The qtipbtrick would likely work but it sounds awful for minigames
).
If my explanation is a bit weird and confusing, LMK, I can record a video of me dissasembling a tama(I need to tinker around in a few anyway); sometimes visuals help a lot. (^~^)ゞ
Edit: did a little drawing. This is an approximation of what you'll find. You'll only need to do two snips and maybe trim to fit if it doesn't set properly initially. You'll see how it fits in the shell, don't force anything.
Also, cover the hole where the c button goes to keep out dirt and debris. You don't want to cause unnecessary damage to the contact underneath. Washi tape or a good sticker should suffice.
Edit 2: as easy as a temporary fix like this feels to me, obviously do this at your own risk.