Only dye your hair if you feel comfortable with it, as well as if you are proficent ant dying hair in a cramped hotel bathroom, would be my suggestion. You are in quite a pickle there with your options as the con is too close to purchase a wig in time, but the last thing you want to do is get a messy dye job on your hair and be forced to live with it while it slowly comes out.
Other than that, I would suggest doing an up-do of sorts and hidingthe majority of your hair under a hat of your choice. You could go with a fez, stenson, or any crazy hat that you want, really; the Doctor's new motto seems to be "I wear a ____ now, ____s are cool!" so you can get away with anything!
Also, check out the vendors in the dealer's hall, as there might be a wig company there selling merchandice and you might find the perfect fem!11 wig there. You never know~
In the end though, it's all about having fun, so who cares if you dont have every last detail perfect <3 I hope you have fun, and please post pictures for us to see how your guy's cosplays come out!