U.S. Priority Mail is about the best and most reliable delivery method. It usually takes only 2 days and there aren't any rural surcharges like with UPS.
There is a surcharge for sending an extra long package if the gun isn't broken down though, but that's only an extra $3.50 or so.
Double boxing, i.e. - putting it inside a box within a box is recommended. These can be aquired at a local gunshop. Use foam, paper or bubble wrap to wrap around the entire gun and to protect the stock.
Most letter carriers know the local residents on their route and when and how to best deliver such a package. Especially if the customer lets him know that it's coming and what their delivery preference is.
Ask the postal clerk to mark the package "fragile", and if asked about the contents, tell them it's an antique muzzle loading firearm which modern replicas qualify as being. Being fully insured and sent by Priority Mail gets the best service IMO.
Adding delivery confirmation provides an easy way to track the rapid progress of delivery.
The gun can always be broken down and sent in 2 packages if someone felt that they're not able to package it securely enough whole.
Some gun builders will ship more expensive rifles in a specialized handmade crated box, but I don't think that's absolutely necessary if it's padded well enough.
I've never had a problem shipping a gun through the U.S. Mail. Because it's shipped so rapidly, usually by air under a postal contract with Fedex, and it's being tracked all along the way, there's less chance for it to be lost or mis-routed. Also, I believe that because it's fully insured and protected by U.S Postal laws, there's less chance of damage or employee theft. Postal workers are usually career employees and many are military veterans with a high sense of duty and professional responsiblility to their job. I've read about so many horror stories shipping with private carriers and difficulties getting insurance claims covered for lost and damaged goods. Whether a gun needs to be sent to Alaska or anywhere else in the U.S., it's the U.S. Postal Service that I have the most faith in, especially Priority Mail service. They've virtually always delivered undamaged and on time for me.