If you really WANT to change genders via wild shape, yah I guess you can.
Question: Are you ready to set yourself up to be the target of rude jokes for the next month?
As a DM, I've had to squash some in-game tomfoolery when it began bleeding out-of-game to become double-entendre and insults. Unless your group is (1) unusually mature and (2) very circumspect with their speech - each and every member - I recommend you just let this idea fade into the background.
or 3) Everyone is incredibly immature and enjoys double-entendre and insults
or 4) Everyone is a mature misanthrope with thick skins
or 5) Some are verbal Sadists and some are verbal masochists and one of the masochists are playing the said druid
or 6) Everyone simply doesn't give a Sh*t
or 7) You really enjoy watching people get insulted at your gaming table
or 8) You are the player and you think being the target of rude jokes is the high point of comedy (fart jokes, for example, are usually crowd-pleasers despite our 'advanced' civilization)
or etc.
But yeah...anyone who as ever seen a girdle of femininity and masculinity in play knows where this going.