Turn pull-up into pull-down
The best way is (as you suggest) to remove the pull-up from the PCB and fit a pull-down elsewhere. But, you could try just fitting a pull-down resistor of much lower value than the pull-up. The two resistors will form a voltage divider, but with one resistor much lower in value than the other, the lower value will "win" and pull the pin down. The disadvantage of doing this is higher power consumption then the MCU pulls the pin HIGH. Make sure the pull-down resistor does not draw more current from the MCU pin than it can supply (check the datasheet) when pulling HIGH.