http://www.handgunlaw.us/
I also suggest checking with local laws/regs as others have shared. Personally, I have been in states, in the past, that did allow non-res permits/licenses, and I have done so. I mean it was less monies for the non-res license/permits, and I was traveling at the time.
Today, I do not travel much, and where I reside, I have a lifetime CCW, and according to what I have read on the link provided above, and speaking with LEO's and such, I am legal elsewhere.
Keep in mind, with no disrespect to LEO, the fact of the matter is, with so many laws, it is darn difficult for LEO to know what is what. Keep it simple, and be civil and polite to LEO. This also covers your rear-end in the event something becomes serious.
Also, if matters come to worse, a jury of one's peers, does not mean 12 folks that think, believe in, raised the way you were, or vote as you do, etc.
Meaning cover your butt, playing the legal game, and have a resident permit/license. This does not mean one cannot later get a non-res.
About a month or so ago, the last of many non-res permits I had, expired. I let them all (non-res) expire. I just have the lifetime, a simple card, with no picture in my wallet.
Good thing, as the older I get, the uglier I get and the non-res one with picture...reminded just how old I am getting, and uglier with age.