Actually, we transport airsoft weapons via airlines all the time, you just have to know the rules. Cases get expensive but they're well worth it.
Here's how you do it, it's exactly the same to transport an inert prop as it would be to transport an airsoft gun.
http://www.midwestairsofters.com/forums/index.php?topic=16079.0
And a definitive list of items explicitly allowed and prohibited by the TSA on aircraft.
http://www.tsa.gov/traveler-information/prohibited-items
As a side note, it is technically illegal, and in all cases a good grounds for reasonable suspicion for LEO contact, to conceal your identity in public, with a mask, helmet, hood, or anything of the such. I wouldn't feel bad wearing the armor in public, but the helmet is a little dicey.
In regards to the orange tips:
THis IS a law, but only in order to sell a gun; it must be marked with a "non-removable blaze orange or red indicator at the muzzle end, covering no less than 1/4" back". There is no law stating that your replica gun is illegal if you have no orange tip on it. But this often works sort of like, for example, a hypothetical law that said you can smoke marijuana, but you can't buy it or grow it.
Keep in mind though, that if you're going to carry anything in public, orange tip or no, it's easy for anyone, especially some jumpy yahoo with a new concealed carry permit in a Stand Your Ground state, to get away with causing some real serious trouble. I would not personally recommend carrying a replica gun anywhere in public except as part of a display where you would be expected to do so, for example, a squad of ODSTs with battle rifles marching behind a replica Warthog in a 4th of July parade or somesuch.
Because the definition of "crime" is getting dicey, and anything that appears to be a weapon counts as a weapon during the commission of a crime.