if I'm getting this correctly then the 10 game limit exists because while the Micro SD holds the roms, the Sky3DS cart itself holds the saves and headers and whatnot to pass as a real game, and it may have a memory limit or something equivalent
given that I have a tool that I can plug into my laptop which can dump, restore, and delete saves from any DS/3DS game cart, in theory I could put the Sky3DS into it and use that button to shuffle between games and delete saves to make space for other games
obviously I don't know a thing or two about how the cart actually works so there's a slim chance that this would work at all but its just an idea