I have a show kit that I take with me to the show.
Baby wipes, preferable detergent and scent free since the detergent can leave a slight crust, for unexpected feather messes
A spray bottle with just plain water for tougher messes and also in case it is very hot. A nice mist does a hot bird a bit of good
Old rags for tough messes that involve the spray bottle and also for cleaning really dirty feet. Stressed out birds can get diarrhea which sticks like glue to feet when it dries.
A small bucket in case I need to clean some really dirty feet. Just fill the bucket with warm water and dip the rag in it.
A set of nail trimmers, though you should trim toenails and spurs about 3 days before the show. I bring the trimmers in case of snagged toe nails and spurs that can bleed.
Stiptic powder just in case, or corn starch if I am out of stiptic powder. I have had a cock break a spur in the show coups before and it wasn't pretty.
A first aid kit for both me and the birds that has bandaids, neosporin, gauze, etc. Just in case, sometimes stuff just happens.
Baby oil for the combs and feet though it does leave an oily residue it leaves a nice shine, I don't prefer Vaseline since it can gunk up the head feathers a bit when it dries.
I also bring a product called ProGroom which I spray on the feathers of the birds about an hour before showing. It smells horrible, but it leaves the feathers so soft and shiny it is surprising. It is a favorite of dog shows and does not remove any of the essential oils from the feathers.
Don't forget to bring food and water for your birds. Some shows don't provide food, so it is always good to bring your own.
Be sure you transport your birds in nice clean carriers with deep fluffy bedding to help keep them clean. Keep your show coups clean as well. It helps to go through every hour or so and scoop the piles of poop out. It will make a big difference in the end.