Disassemble a USB mouse and carefully remover the circuit board.
Locate the small micro switches. A 2 button mouse will have 2 and a 3 button mouse will have 3.
One each for the left, right and center mouse buttons.
On the underside of the circuit board locate the micro switch connectors for each switch
Using a soldering iron unsolder the connectors of the micro switches.
There are usually 3 connectors for each switch. Be careful with the iron, it gets very hot.
Use some light weight wire and solder that in place of the micro switch. Usually only 2 of those connectors are used.
Test to see which ones are used on your circuit board by plugging the USB cable into the computer and use a small piece of wire to touch 2 connectors and see if the computer responds like a mouse click.
Solder the other ends of the wire to the 2 connectors on the arcade button.
Do this for each of the 3 buttons. Be sure and allow enough wire to mount the buttons in the booth where you want them.