Here is a short list of Mississippi Outfitters who specialize in Hog Hunts. Darden offers a "Traditional Hunt". That means they catch the hogs live using dogs. Hogs can then be killed or transported depending on the wants of the hunter. A friend has used them and was very complimentary of the outfitter and his accomodations.
As far as bringing a weapon into the country I know nothing. Your safest bet would be to contact US Customs or the BATF.
Darden Hunts is located in Centerville. That is about 2 1/2 hours drive from New Orleans and 1 hour from Baton Rouge. In the Baton Rouge area there is a Bass Pro Shop and a Cabela's Outfitters. Both are well worth the time for a daytrip if you enjoy fishing or hunting.
Thank you Remgirl and BTR568. July is a bit early for me as I am booked in for Germany then and Have the CLA Game fair to show at, hoping to promote my South African outfitter. I have Africa in September/October time. I think this will be a project in 2011, when I also plan to visit with an old oilfield buddy in Lake Charles, La.