Buy a cheap box truck, find someone desperate. Offer him $20k to make minimal stops and blow all the weigh stations.

Since the question specifically asked about mailing, I specifically recommend one of those hard sided Pelican cases, with the cut-to-form foam inserts.

You'll pay a fortune in postage.

I'm not sure if the postal service routinely scans parcels with a Geiger counter. If they do, you might consider paying an even larger fortune to ship shielding.

The real engineering challenge is the mechanism that triggers the criticality event. Demon core was able to kill the people it killed, because they were using jankety-ass stuff like screwdrivers to hold the hemispheres apart. Getting a mechanism that works reliably when you want it to, and not when you don't is hard. For the first few years of nuclear weapons, it was not allowed to insert the nuclear pits into the bombs until the plane had taken off with positive attack orders. Imagine trying to jimmy a core into a bomb casing in the bomb bay of a B-29 while it's traversing 800 nm of hostile waters to Japan. Sounds crazy, but that's what they did.

Anyhow, mechanisms are hard. It took at least twenty or thirty years to get to something that has a "reasonable" level of safety. And if you see the blue light, you're probably already a goner.

Very very carefully, drop it in a postbox and run!