ok after reading more than i care to.....
nothing to see here, i think
shotguns have a exemption
https://www.law.cornell.edu/cfr/text/15/740.14
and rifles do as well.
https://www.law.cornell.edu/cfr/text/22/123.17
a interesting read
http://huntinafrica.com/usefulinfo/rifleimport
so do not try and take your 20mm canon with kriptonite war heads dove hunting in Argentina but its fine to take your shotgun or bolt action rifle.
form 4457 is still required....
i am not a lawyer, do not believe anything i posted here as you will most probably be rerouted to a out of the way isis held camp and your head will become detached.