I would like to replace the fan of my Dell

I would like to replace the fan of my Dell Dimension 9200 with a new / different one. Dell germany is asking me for 70 euro for a replacement (not service, just the part) - nice joke I thought.
The Dell Dimension (and other models) is using a non-standard connector for the CPU fan. Its a 5Pin connector with 4Pins used. As its using 4Pins, I am confident its a PWM controlled fan.
The question left is, which Pin of that fan connector on the Dell Mobo is serving what exactly? Now looking at the original cable connection, Black and Red most likely are GND and +12V, but what about Blue and White?

My guesses which I would love to get confirmed:
Blue = PWM (aka control), White = RPM (aka sense)

If replaced by a generic (but similar specced) PWM fan (e.g. Arctic F12 Pro PWM) and properly rewired according to my guesses like below, will the machine work, will it complain, will it burst in flames?

black - black
red - red
blue - blue
white - yellow