Yes you should. It's the same as saying there is a dress code at a office. The office won't pay for a wardrobe. You should wear black shoes, and you'd be paying for them. I think they should give you plenty of time to get new ones, so like the next day tehy shouldn't be harping at anyone.
I think dying the ones you have is the best idea. Cheap, same boots, and all done. Shoe repair places can dye them usually cheap too. Otherwise.. sharpie markers are cheap too! LOL