See, you seem to be coming up this with some pretty badly crossed concepts. If your mind was a group of pipes, i'd whistle and say somethig like "boy, you've had some real cowboys in here, heaven't you." Your main two incorrect premises are as follows. Number one, women do not actually share some sort of shared mind space, we aren't a zeitgest collective mind speaking through 1,000 mouths. Each one of us is shaped by our own experiences & even though we share the general concepts with each other, none of us actually share those eqperiences universally. As such things like writing skill has absolutely nothing to do with gender.
Secondly, this idea that WW is some sort of universal female character is just plain up silly. She is a character, who is also incidentally female. To ask if a man can write a WW story as well as a female, is as asanine as asking can a man write a Ms Martian story as well as woman can: Of course he can. We are female, not magical earth goddess made flesh... Just straight up flawed, squishy, mildly disturbing human beings.
Fun fact, though: Most people who read a piece of fiction cannot tell the difference between a male or female writer if they aren't told. Heck, not to bad mouth Gail Simone & the nonsense that is WiR, but look at how many times Gail broke her own rules of fridging & no one mentions it, but as soon as a male writer does anything even close the accussations of "fridging" start. The fact is that in exactly the same way you can convince people that 2 identical products taste different based on brand recognition, people have been shown to not actually be able to tell the difference between male & female writers (but will still judge the content based on who they've been told the author is).
So no, i don't think that gender has anything to do with writing skill.