I have been in this exact situation, years ago when I first started running and for some reason was getting a lot of bruised/lost toenails. Take a small piece of white first aid tape, cut it in the shape of a toenail, and stick it on where your toenail is missing. Then paint it as you would a normal nail. No one will know the difference, and you can peel it off when you get home. Be forewarned that polish does not last as long on first aid tape as it would on your nail, but you should be able to get a day or two out of it without chips. Also, remember that when chips do occur, the base color is stark white - so it's best to avoid very dark polish colors. But it should get you through the night without any danger to your growing nails or nail beds.
