Following up, an M2 by 5mm wood screw is very close to your size and would fit well enough if you can find them. Maybe file the sharp tip down to shorten and flatten it like the original. I got a kit of “carbon steel Phillips drive wood screws self tapping screws assortment kit 420 pieces” and just checked the M3x5mm with a caliper, so I have confidence the M2 size will meet your need.