I ship many many burms every year and I can give you the run down on how I do it.
One of the first things I check are the temps-where I live, where the buyer lives and in Memphis, Tenn (our main Fedex hub here on the east coast). After making sure temps are not going to get too low or too high then if able to be shipped I make adjustments if needed with a heat or cold pack depending on time of the year. I then contact my customer to confirm shipping on that particular day (we ship Mon-Wed) and will usually have my Fedex label printed and give them the tracking number-Fedex does not charge for shipment until the label is scanned so if something comes up and the customer cannot be home to receive the package then there's no loss. I am Fedex and Delta verified so no problems there. Around 6pm in the evening I get the burm that I am shipping and check it over to make sure its good to go, snap a few pics of it then get it ready to ship. I use 12x9x6 foam insulated boxes. I put the snake in a bag and tie, knot, and tape it. I do the label the bag also. There is also some type of substrate in the bag whether it be shredded newspaper or a papertowel to absorb any mess if the snake decides to urinate or worse in flight. (I never feed ours a day or two before I ship to reduce the risk of a regurge). I place the bag into the box with shredded newspaper under, all around, and on top of it. The box will also have airholes punched into the sides. I also include a feed/shed chart, a business card with website and phone number, and a genetics rundown on the the snake and its parents. Our Fedex guy is great-he stops by the house around 7pm and picks up our packages-after he leaves I send the pics and the message that the snake is on the way to the buyer.
When the snakes arrive I recommend either removing them carefully (baby burms for example can be nippy) or open the bag and let the baby make its way out into its new enclosure. Have fresh water and hides available-the new one will probably spend some time checking out every corner of its new home so I would give it a few days to settle before handling and trying to feed. If you have any questions or concerns call the breeder and ask!!! And also let the breeder know it has arrived (thats a personal one for me-I tend to stay up all hours of the night and pace by the phone waiting to hear the snake arrived and they are happy with it)
I agree that no vet visit is necessary unless you see some signs of a problem.