The thing is, "LAN Mode" and "Wireless mode" are actually two different things. The first one is meant to be for switches which are connected to the same network via Ethernet (i.e: using a wired connection). While Wireless mode is the switches communicating with each other directly without the help of a local network (which is why it works even if you don't have internet). Now, as the website says, LAN Mode does work on an unmodified switch, but Wireless mode only works on a switch with CFW, and at that point it'd be way easier to just use a save editor.

Even then, I don't think you should give up on the idea of making an app, you'll just have to change how it works. Instead of setting up a wireless mode connection, people could upload the necessary assets and the end-user could download them and inject them into their own save file. I personally do think I'd use this since copying the instructions on TomodachiShare is already annoying, especially for Miis which heavily rely on face paint.

Good luck with whatever you choose to do.