If your coming here in June, I'd suggest looking at a hog hunt. Here's
a link to where the hog problem is. That should provide a start.
As to guns, yes - many guides will rent/loan you a gun.
If you wanted to go to Florida,
here is someone to use (I haven't used him, but know some people who have) who will have a gun for you to use if you can't bring your own and he's within a couple of hours of Miami, Disney, and Cape Canaveral.