I have a Retro-bit Retro Duo console which I bought from eBay a number of years ago. I actually got it to play Famicom games on it before I got a famicom.
It comes with 2 controllers however you can use official SNES controllers for it if you prefer. There are some games that won't work on it however it never bothered me. I don't have an Everdrive to try out however I cannot see why it wont work.