I think every deer farm should own a dog, one that is just as excited as you are when the first fawn hits the ground. Our black lab gives GREAT care and makes sure our fawns stay clean. Just giving her a milkbone treat afterwards makes everyone happy here!
If not, I agree with baby wipes, dipped in warm water and then swirled around under the tail. Keep dipping it in warm water and then also down the inside of the legs and up the underside of the tail to the tip, just like the momma would do.