mednafen doesn't have a gui (grahpic user interface), what I do to test games is drag a rom into the .exe. That will launch the game and emulator. When you set it up through hyperspin (set up the directory to the exe and the rom directory) hyperspin will have no issues launching it.
When you are testing, you need to pres alt + shift + 1 to setup player one's controls (alt +shift + 2 for player 2) (you have to press each button direction 2x, this was done so you can have two things controlling player one, i.e. arcade panel and joypad).
If you want it fullscreen you need to go into the "ini" file and edit it. If you use 5 and 1 for start and select, then you need to edit the ini to not have 5 and 1 control the save states.
Remember, to test it by draggin the rom into the exe.
Mednafen is the most reliable emulator for several systems and lets you do fullscreen for some system including game gear and lynx (I think)