It also came bundled with Alien Front Online so maybe it'll be a bit cheaper that way than searching specifically for the mic, or a game that was more popular with it like Seaman? I can't check auctions rn but might be worth a try.
This seems to be a pretty basic button. Not really worth gutting an entire controller for it imo (without seeing your design anyway). Someone could probably 3D print you one as an alternative if you don't have anything remotely close to a replacement.
@geobot9k if you see this, did you happen to design the back part too? Probably wasn't at all necessary and quicker to spraypaint anyway, but I have the perfect two filaments for a NES color designed case so ¯\_(ツ)_/¯
For the SNES Mini, the best you're going to find (probably) is the one in benheck's book from a while ago. There's a few errors but they have been noted and changed thru the community. There's a free pdf of it around somewhere. At the very least it's a good start.