PWM on negative pin to positive (the common) PWM for a fan's control pin
Your current fan is likely connected with a low side N Channel MOSFET driver as shown below:



Fan PWM inputs are typically active low and pulled high internal to the fan.  That way the fan runs at full speed when the PWM input is not connected.  I could not tell from the data sheet if this is the case for your fan.  If it runs at full speed with the PWM input floating and stops when you pull the PWM to GND, then it probably is.  This is the general PWM info from the fan manufacturer.

In any case, the fan PWM input does not have high current draw, so it can be directly driven by the pin on the fan connector that is NOT connected to the power supply.  That should pulse low to control the fan speed.  The ground on the fan also needs to be connected to the ground on the power supply.