I don't believe such a browser exists unless every file explorer has functionality like that which I'm not aware of, but my advice to you:Move files from an r4 card to the sd card thats the in a 3ds.so i dont have to keep unscrewing the back and taking the sd card out.because of the bans ppl have getting ive switched my wifi off so i cant use ftp or freeshop.
you would need a DLDI driver for that specific card, (which is mostly available on the NDS homebrew) i once asked for something like this, people had mentioned that this couldn't be done because the 3ds arm didn't add access or blablablaI just checked with my r4i 3DS and GodMode9, you can't access the r4's SD card because it only sees the fake NDS data (in my case, it thinks it's a copy of Narnia's the Caspian prince game).