Still fear of de-soldering lol
Found two new things that might help:
1. When I load/boot IK+ from floppy, I should press the joystick/mouse button of the left port to continue.
Pressing the joystick button of the right port won't let me to continue to play the game.
After that, I can play the game with both joysticks though.
2. The left port has stronger/sturdy pins than the right board, doesn't bend at all.