The iCade cabinet comes with arcade stick with 8 push buttons with micro-switches which are good enough for my project.
Since iCade was created for iPad the stick is connected to Bluetooth board which uses proprietary protocol. I tried to configure it via Bluetooth but it was not working as expected so I decided to unplug all the micro switches and ditch the board.
Ideal replacement was zero delay USB encoder board found on eBay for less than $10:
Since you will receive connector cables you need to assemble it to the board, stick and buttons. Good thing is that when you disconnect stick connectors from Bluetooth board you can connect them directly to the new USB board. Only thing you have to fit yourself are the buttons. I had to use screwdriver to pry the connectors a bit to fit to the switches but at the end it fit perfectly. I used pieces of isolation tape just to protect the connections from loose wires.
You will still need to find good position for the board in the iCade bottom plastic casing since it will not fit into Bluetooth boards position.