There MIGHT be more to this than you think. On all current computer fans the female connector on the end of the wires has two ridges running down one side. These enclose Pins 1 to 3. IF it's a 4-pin connector, Pin 4 is outside the range of the ridges. On the mobo MALE header, there is a plastic "tongue" sticking up beside Pins 1 to 3, and those two ridges fit on the outsides of that tongue. That way you cannot connect them wrong.
Now, you refer to those ridges as "tabs". This leads me to suspect that the header on your old mobo does NOT have that same male fitting with the tongue. Instead it MAY have a sort of "socket" of plastic with the pins inside that sleeve. And that sleeve has some slots in one side that match "tabs" or ridges on the outside of the old fan's connector. Is that right? Of course, that also ensures that you can only connect one way.
HOWEVER, the fact that the old fan and mobo use a connector DIFFERENT from what has become "standard" means it is also possible that the PINOUT they use does NOT match what is the standard today. IF you can figure out what the old system pins do, here is how the current "standard" 4-pin fan connector is wired. NOTE that this is for the newer-design PWM style of motor, and NOT what an older 3-pin simpler motor (speed controlled by varying Voltage supplied) does. Recall, Pins 1-3 are between the ridges, Pin 4 is outside.
Pin 1 = Ground
Pin 2 = Fixed +12 VDC power
Pin 3 = Speed signal (5 VDC pulses, 2 per revolution) generated by the motor and sent to header on this pin
Pin 4 = PWM control signal, approx 22 KHz freq, Pulse Width Modulation signal, 5 VDC peak)
Unless you can verify that the mobo header DOES supply those signals in some form, you may not be able to use that new fan, even with custom re-wiring.
Since this is from an older system it may pre-date the introduction of the 4-pin PWM fan design. In that case the old fan likely is of the 3-pin Voltage Controlled design, and you might be able to rig a modern fan for that system IF you know what all 4 pins of the header on the old mobo do.