Kymaera has a fully mappable input system where you can assign any input (keyboard,mouse,joystick) to any FE function. Kymaera also supports using a combination of keys. For example, I use the P1B1 + P1B2 keys together to add a game to my gamelist, so I don't accidently add a game to my list.
The input system can use for example B1 OR B2 to trigger a system input, or it can use B1 AND B2.
Using this system, you can use a button like a shift function, so to answer your question, Yes, you can run the entire FE using 1 button and a Joystick. Use the button as a shift button, and have the Joystick doing double duty to navigate the game list, catagories, emulators, and launching the game. Like this:
^
<- - > O
v
up = move to the previous game in game list
down = next game in game list
left = page up in gamelist
right = page down in game list
B1 + up = next catagory
B1 + down = exit FE
B1 + left = next emulator
B1 + right = add to favorites
B1 = launch game
You could even have an "add game to favorites list" button and an exit button.
If you wanted to get really fancy, you could do things line this:
up + left + b1 = Exit FE
So you could move the joystick to the upper left and press B1 to exit the FE.
-PMF