its no problem as long as your pcb that you're using is common ground (there's a bit more wiring dinks if it wasn't)
and there's also a bit of heavy case modification
if i remember right, the happ/IL/Suzo sticks use quick disconnect terminals instead of wire harnesses
you're going to have to pull out your soldering iron and figure out which one the wires leading up to the switch is the ground and signal. from there, link the ground wires together and follow the JLF pinout on the other side.
You're also going to have to modify the case to accept a japanese joystick. That requires a few woodworking tools (if its a wood case)
just out of curiosity, what kind of stick do you have?
because you said american, i'm going to assume either AIAB, MAS, or those old school pelican sticks