I can't speak to the level of radiation of uranium nukes, but I can say that every container headed towards the US is now put through a radiation portal monitor http://en.wikipedia.org/wiki/Radiation_Portal_Monitor
that detects a wide range of radiation. The DOE is pretty extensive in their tests with a wide range of test objects that emit various types of radiation.
The program was (is?) called the SLD (second line of defense) and put these scanners at every foreign port where US shipments are loaded. I was personally at a number of these port installing support equipment so I saw them in action. Any box that tripped an alarm, like a box full of bananas, would be opened or scanned with xray to confirm the load matched the manifest.
As per the specific radiation being detected, again I don't know, but a quick google search shows that enriched uranium as common for dirty bombs due to it being easier to manufacturer, etc. And since SLD was primarily designed to look for dirty bombs I am assuming this type was built into the detectors.