Do we need to know "how" Odo knew the Vulcan pinch? He's a law enforcement officer, so probably knows all sorts of aggressive and defensive moves from various species. We don't need to know that he learnt it from some Vulcan guy a few years back, do we?
As for why use it on the female guard... I assume (hope!) chivalry is still alive in the 24th century and Odo didn't feel it really appropriate to punch a woman out. He's nice like that.