The disc could then just be a caddy for a micro SD memory card, which when inserted on the disc slot would promptly launch a game stored in there.

Selecting games from a virtual library never has the same kick as when you insert a cartridge or a dis[ck] into a machine and have it boot from that.

Edit: I also realized you may as well cut out the memory card and just have each "fake" disc encode (perhaps optically) a little ID which the machine could read (perhaps a cheap camera) and associate to a game already stored in the machine's internal memory.